Academia.eduAcademia.edu

Outline

Title
Abstract
FAQs
Presentation of the Material
Characterisation Results
Parry's Analytic Implication
Fde with Strict Implication and Classicality
References

Reasoning with Relevant Epistemic Logics

Profile image of Pietro VigianiPietro Vigiani

2025, Reasoning with Relevant Epistemic Logics, PhD Dissertation, Scuola Normale Superiore

Abstract

The present dissertation investigates the relationships between classical and nonclassical logics within a common logical platform, in which it is possible to address philosophical questions. More specifically, the focus of the dissertation lies in applications of relevant logics to problems in formal epistemology, such as the problem of logical omnisicence, the distinction between explicit and implicit beliefs, and the modeling of belief revision. As the main contribution of the present work, I devise so-called contextual modal logics, i.e. modal logics where modal operators individuate the range of application of a given logic, to be chosen from the class of extensions of weak relevant logics. In this way, I argue that it is possible to adequately formalise the context-sensitivity of reasoning, a feature which arises when we confront reasoning about the factual and the epistemic domain. Contextual modal logics are presented both semantically and proof-theoretically, by means of Hilbert-style axiom systems. The language of the logics is modularly extended, from the basic relevant language, so as to include topic sensitive operators, implicit belief operators and dynamic operators. Characterisation results are obtained for all extensions of the logics in the contextual modal family.

FAQs

sparkles

AI

What are the challenges of logical omniscience in epistemic logic?add

The dissertation identifies that standard modal logics suffer from logical omniscience, as agents may have knowledge resulting in incorrect beliefs regarding logical truths. This discrepancy is highlighted through examples showing contradictory mathematical propositions believed by ordinary agents.

How do contextual modal logics address logical closure properties?add

Contextual modal logics propose a framework where closure principles are regulated by relevant logic, rather than classical logic, enabling a more nuanced epistemic competence. This approach allows for the incorporation of cognitive limitations in belief systems.

In what manner does relevant logic support epistemic reasoning?add

Relevant logic provides a flexible framework for modeling epistemic reasoning, addressing closure properties that fail classic standards of rationality, especially concerning ordinary cognitive limitations in belief aggregation and combination. For instance, belief in implications can fail if relevant contexts are ignored.

What is the significance of the Routley-Meyer semantics in epistemic logics?add

Routley-Meyer semantics allows for the interpretation of non-classical logical relationships, emphasizing weak closure properties suited for modeling epistemic reasoning. This framework proves vital in differentiating between logical states and non-logical states of information.

How do topic-sensitive logics contribute to overcoming logical omniscience?add

Topic-sensitive logics regulate epistemic closure principles by imposing requirements on topic inclusion across beliefs, thereby preventing agents from making equivalent substitutive inferences under conditions leading to logical omniscience. This addresses cognitive limitations faced by agents when updating beliefs.

Related papers

Abstract modal logics
Ramon Jansana

Studia Logica - An International Journal for Symbolic Logic, 1995

Abstract.

View PDFchevron_right
"Contextual Epistemic Logic"
Franck Lihoreau

In C. Degremont, L. Keiff and H. Rueckert (Eds.), Dialogues, Logics and Other Strange Things., 2009

One of the highlights of recent informal epistemology is its growing theoretical emphasis upon various notions of context. The present paper addresses the connections between knowledge and context within a formal approach. To this end, a "contextual epistemic logic", CEL, is proposed, which consists of an extension of standard S5 epistemic modal logic with appropriate reduction axioms to deal with an extra contextual operator. We describe the axiomatics and supply both a Kripkean and a dialogical semantics for CEL. An illustration of how it may fruitfully be applied to informal epistemological matters is provided.

View PDFchevron_right
A note on some explicit modal logics
Eric Pacuit

2006

Artemov introduced the Logic of Proofs (LP) as a logic of explicit proofs. We can also offer an epistemic reading of this formula: "t is a possible justification of φ". Motivated, in part, by this epistemic reading, Fitting introduced a Kripke style semantics for LP in . In this note, we prove soundness and completeness of some axiom systems which are not covered in [8].

View PDFchevron_right
Indicative Conditionals and Dynamic Epistemic Logic
Wesley Holliday

Proceedings of the Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK XVI), 2017

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45.

View PDFchevron_right
Term-Modal Logics of Evidence
Igor Sedlar

Term-modal logics are versions of first-order modal logic with modal operators indexed by terms of a first-order language. This paper outlines an evidence-based epistemic interpretation of a simplified version of the framework. It is argued that term-modal logics are particularly useful in analysing problems involving reasoning about complex properties of evidence. Examples from the debate between externalists and internalists with respect to justification are chosen to demonstrate this point. The main technical result is that the term-modal framework is able to emulate monotonic modal logics and epistemic logics with awareness. This result suggests that the framework is suitable for combining justification logics and evidence logics, the two major current families of logics that deal with evidence explicitly. A corollary of the main technical contribution is a decidability result for a simple fragment of the term-modal framework.

View PDFchevron_right
A Framework for Logics of Explicit Belief
James Delgrande

Computational Intelligence, 1995

The epistemic notions of knowledge and belief have most commonly been modeled by means of possible worlds semantics. In such approaches an agent knows (or believes) all logical consequences of its beliefs. Consequently, several approaches have been proposed to model systems of explicit belief, more suited to modeling finite agents or computers. In this paper a general framework is developed for the specification of logics of explicit belief. A generalization of possible worlds, called situations, is adopted. However the notion of an accessibility relation is not employed; instead a sentence is believed if the explicit proposition expressed by the sentence appears among a set of propositions associated with an agent at a situation. Since explicit propositions may be taken as corresponding to "belief contexts" or "frames of mind," the framework also provides a setting for investigating such approaches to belief. The approach provides a uniform and flexible basis from which various issues of explicit belief may be addressed and from which systems may be contrasted and compared. A family of logics is developed using this framework, which extends previous approaches and addresses issues raised by these earlier approaches. The more interesting of these logics are tractable, in that determining if a belief follows from a set of beliefs, given certain assumptions, can be accomplished in polynomial time.

View PDFchevron_right
Modal logic, fundamentally
Wesley Holliday

Advances in Modal Logic, 2024

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices L equipped with an antitone operation ¬ sending 1 to 0, a completely multiplicative operation □, and a completely additive operation ◊. Such lattice expansions can be represented by means of a set X together with binary relations ◁, R, and Q, satisfying some first-order conditions, used to represent (L, ¬), □, and ◊, respectively. Indeed, any lattice L equipped with such a ¬, a multiplicative □, and an additive ◊ embeds into the lattice of propositions of a frame (X, ◁, R, Q). Building on our recent study of fundamental logic, we focus on the case where ¬ is dually self-adjoint (a ≤ ¬b implies b ≤ ¬a) and ◊¬a ≤ ¬□a. In this case, the representations can be constrained so that R = Q, i.e., we need only add a single relation to (X, ◁) to represent both □ and ◊. Using these results, we prove that a system of fundamental modal logic is sound and complete with respect to an elementary class of bi-relational structures (X, ◁, R).

View PDFchevron_right
Term-Modal Logics of Evidence: Some Preliminary Observations
Igor Sedlar

Term-modal logics are versions of first-order modal logic with modal operators indexed by terms of the language. This article outlines an evidence-based epistemic interpretation of the term-modal framework. It is argued that term-modal logics are useful in analysing scenarios involving complex properties of evidence. Examples from the debate between externalists and internalists with respect to justification are chosen to demonstrate this point. The main technical result is that the term-modal framework is able to emulate monotonic modal logics and epistemic logics with awareness. This result suggests that the framework is suitable for combining justification logics and evidence logics, the two major current families of logics that deal with evidence explicitly. A corollary of the main technical contribution is a decidability result for a simple fragment of the term-modal framework.

View PDFchevron_right
Special Issue: Advances in Philosophical Logic Preface
Heinrich Wansing

Studia Logica

View PDFchevron_right
Semantical investigations on some weak modal logics. Part I
Andrzej Pietruszczak

Bulletin of the Section of Logic

In this paper we examine weak logics similar to S0.5[□Φ], where Φ⊆S0·5. We also examine their versions (one of which is S0.5 rte [□Φ]) that are closed under replacement of tautological equivalents (rte). We have that: S0.5 rte [□(K),□(T)]⊊S0·9, S0.5 rte [□(X),□(T)]⊊S1, and in general, if Φ⊆E1, then S0.5 rte [□Φ]⊊S2. In the second part we shall give simplified semantics for these logics, formulated by means of some Kripke-style models. We shall also prove that the logics in question are determined by some classes of these models.

View PDFchevron_right

References (248)

  1. Igor Sedlár and Pietro Vigiani. "Relevant Reasoners in a Classical World". In: Advances in Modal Logic, Volume 14. Ed. by David Fernández Duque, Alessandra Palmigiano, and Sophie Pichinat. London: College Publications, 2022, pp. 697-718. Chapter 4.
  2. Igor Sedlár and Pietro Vigiani. "Epistemic Logics for Relevant Reasoners". In: Journal of Philosophical Logic 53 (2024), pp. 1383-1411. Chapter 5.
  3. Pietro Vigiani. "A Hyperintensional Logic of Non-prime Evidence". In: Jour- nal of Philosophical Logic 53.3 (2024), pp. 761-788. Chapter 6.
  4. Pietro Vigiani. "Relevant Epistemic Logic with State-Sensitive Topics". In: Synthese 205.35 (2025), pp. 1-28;
  5. Pietro Vigiani and Thomas Macaulay Ferguson. Contextual Entailment and Containment: A Ternary Approach to Information and Topic Inclusion. Under review. Chapter 7.
  6. Igor Sedlár and Pietro Vigiani. "Relevant Reasoning and Implicit Beliefs". In: Logic, Language, Information, and Computation. Ed. by Helle Hvid Hansen, Andre Scedrov, and Ruy J.G.B. de Queiroz. Cham: Springer Nature Switzerland, 2023, pp. 336-350;
  7. Igor Sedlár and Pietro Vigiani. "Explicit and Implicit Belief in First Degree Entailment With Strict Implication". In: New Directions in Relevant Logic. Ed. by Having explained some of the main conceptual features of C.L-models, I sum- marise below some of their formal properties. In particular, note that Condition (W9) allows one to make fine-grained distinctions at the level of semantic entail- ments in C.L-models. As a consequence, modified versions of the semantic deduction theorem are provable (cf. Lemma 3.4).
  8. Lemma 3.2 (C.L-heredity). For all M ∈ C.L and all φ ∈ L Rel : φ M ∈ S(↑).
  9. Proof. The result is established by virtually the same argument of Lemma 2.1. Lemma 3.3 (C.L-flatness). For all M ∈ C.L, all w ∈ W and all φ, ψ ∈ L Rel : 1. M, w |= t;
  10. M, w |= ¬φ iff M, w ̸ |= φ;
  11. M, w |= φ ⊗ ψ iff M, w |= φ ∧ ψ;
  12. M, w |= φ ⊕ ψ iff M, w |= φ ∨ ψ;
  13. M, w |= φ → ψ iff (M, w |= φ =⇒ M, w |= ψ);
  14. M, w |= φ ← ψ iff (M, w |= ψ =⇒ M, w |= φ).
  15. Proof. We distinguish cases, where Item 1 holds trivially by W ⊆ L.
  16. The following chain of equivalences holds: w |= ¬φ iff w * ̸ |= φ iff (by Condition
  17. =⇒ ). Assume w |= φ ⊗ ψ. Hence, there are s, t ∈ S such that Rstw, s |= φ and t |= ψ. By Condition (W3) we infer that either s = 0, t = 0 or s ≤ w. By s |= φ and t |= ψ we infer that s ̸ = 0 and t ̸ = 0, as otherwise they would contradict Lemma 3.
  18. Hence, s ≤ w. Similarly, by Condition (W4) we infer that either s = 0, t = 0 or t ≤ w. By s ̸ = 0 and t ̸ = 0 we infer that t ≤ w. By s, t ≤ w, s |= φ, t |= ψ and Lemma 3.2 we conclude that w |= φ and w |= ψ. (⇐). Assume w |= φ and w |= ψ. By Condition (W2) we infer that there are s, t ∈ S, namely s = t = w, such that Rstw, s |= φ and t |= ψ. We conclude that w |= φ ⊗ ψ.
  19. =⇒ ). Assume by contraposition that w ̸ |= φ and w ̸ |= ψ. By Condition (W1) and (W2) we infer that there are s, t, ∈ S, namely s = t = w, such that Rwst s * ̸ |= φ and t ̸ |= ψ. We conclude by Condition (W1) that w ̸ |= φ ⊕ ψ. (⇐). Assume w |= φ or w |= ψ. In order to show that w |= φ ⊕ ψ, assume for some arbitrary s, t ∈ S that Rwst. We distinguish cases. (1) If w |= φ, by Rwst and Condition (W5) we infer interested reader is referred to [152, Ch.2] for further discussion on the inferential grounds on which to accept disjunctive syllogism.
  20. ♢ -□φ ⊢ φ;
  21. □ I φ ∧ □ I ψ ⊢ □ I (φ ∧ ψ);
  22. Proof. Items 1 and 4 are easy consequences of Proposition 7.3.6, while Item 2 and 3 are instances of Proposition 7.3.1 and 7.3.2, respectively. Item 5 is an easy con- sequence of (FDE c 7) and Proposition 7.3.4. Items 7-9 are easy consequences of Proposition 7.3.9. Finally, item 6 is established as follows: 1. □φ 1 ∧ • • • ∧ □φ n ⊢ FDE c □ I ψ;
  23. Proof. (1) =⇒ (2). By contraposition, assume (2) does not hold with counter- model ({s}, V ). Then, take the FDE c -model M = ({s}, W, * , Q, V ) such that W = {s} and R = {(s, s)}. Clearly, we have that M, s |= □φ 1 ∧ • • • ∧ □φ n , since by assumption M, s |= φ 1 ∧ • • • ∧ φ n . However, M, s ̸ |= □ I ψ, since by assumption M, s ̸ |= ψ (note that this is possible only because φ 1 , . . . , φ n , ψ are propositional formulas). Hence, we conclude by Theorem 7.8 that (1) does not hold. (2) =⇒ (1).
  24. Assume (2). Hence, □ I φ 1 ∧. . .∧□ I φ n ⊢ FDE c □ I ψ (otherwise from the counter-model (S, W, * , Q, V ) to the latter we can extract the counter-model (W, V ) to the former). By Proposition 7.4 (item 5), □φ 1 ∧ . . . ∧ □φ n ⊢ FDE c □ I φ 1 ∧ . . . ∧ □ I φ n . Hence, we conclude that (1) holds. While classical behavior can be forced for propositional variables, this does not apply to formulas containing strict implication, as the following counter-example to a modal version of Proposition 7.5 shows. Proposition 7.6 (Modal closure failure). The following hold: 1.
  25. ⊤ ⊢ K (□¬(p ∧ ¬p));
  26. □⊤ ̸ ⊢ FDE c □ I □¬(p ∧ ¬p).
  27. Proof. It is immediate to verify that (□¬(p ∧ ¬p)) is valid in every Kripke model, as p ∧ ¬p is true at no state in the model. Hence, by completeness of K with respect to K-Kripke models we infer (1). Then, consider the FDE c -model M = (S, W, * , Q, V ) such that S = {s, t, u}, W = {t} Q = {(s, t), (t, u)}, s * = u and t * = t, V (p) = {s, t}. which is established by induction on the complexity of χ ′ . The base case, when
  28. ′ ∈ At holds by setting φ ′ := χ ′ . The induction step cases where the main connective of χ ′ is either ¬, ∧, ∨, →, □, □ L are similar, hence we show only the case χ ′ := □ξ as an illustration. By □ L -(FE [] 8) we infer that ⊢ L [ψ ′ ]□ξ ↔ □(ψ ′ → [ψ ′ ]ξ). By induction hypothesis we infer that there is γ ∈ L RRel such that ⊢ L [ψ ′ ]ξ ↔ γ, which implies by ⊢ L [ψ ′ ]□ξ ↔ □(ψ ′ → [ψ ′ ]ξ), together with □ L -(FE15) and □ L -(FE10), that ⊢ L [ψ ′ ]□ξ ↔ □(ψ ′ → γ). We conclude by setting φ ′ := □(ψ ′ → γ). Finally, the case χ ′ := [ξ]γ is ruled out by χ ′ ∈ L RRel . The following propositions show the closure properties of >. For one, the Ramsey conditional is hyperintensional in both its antecedent and consequent position. This marks a contrast with CK and ConR, where e.g. ψ ↔ χ ⇛ (φ > ψ) → (φ > χ) is admissible. By Proposition 8.4, however, a restricted version of the equivalence rule holds for > in C.F.E [] .
  29. Proposition 8.4 (>-Relevant equivalence). The following rules are derivable in C.F.E [] :
  30. □ L (φ ↔ ψ) ⇛ (φ > χ) ↔ (ψ > χ);
  31. □ L (φ ↔ ψ) ⇛ (χ > φ) ↔ (χ > ψ).
  32. Proof. The following derivations establish the result. Antecedent Restricted Equivalence (1) □ L (φ ↔ ψ) (2) □ L (□χ ↔ □χ)
  33. □ L -(FE [] 1)
  34. □ L -(FE [] 1)
  35. □ L (□φ ↔ □ψ) □ L -(FE [] 1) (1)
  36. □φ ↔ [χ]□ψ (BR), (4)
  37. Wilhelm Ackermann. "Begründung Einer Strengen Implikation". In: The Journal of Sym- bolic Logic 21.2 (1956), pp. 113-128.
  38. Ernest W. Adams. The Logic of Conditionals: An Application of Probability to Deductive Logic. Dordrecht: Springer, 1975.
  39. Carlos E. Alchourrón, Peter Gärdenfors, and David Makinson. "On the Logic of Theory Change: Partial Meet Contraction and Revision Functions". In: Journal of Symbolic Logic 50.2 (1985), pp. 510-530.
  40. Alan Ross Anderson and Nuel Belnap. Entailment: The Logic of Relevance and Necessity, Vol. 1. Princeton Univ Press, 1975.
  41. Richard Bradshaw Angell. "Deducibility, Entailment and Analytic Containment". In: Di- rections in Relevant Logic. Ed. by Jean Norman and Richard Sylvan. Kluwer Academic Publishers, 1989, pp. 119-143.
  42. Sergei Artemov. "The Logic of Justification". In: The Review of Symbolic Logic 1.4 (2008), pp. 477-513.
  43. Arnon Avron. "Hypersequents, logical consequence and intermediate logics for concur- rency". In: Annals of Mathematics and Artificial Intelligence 4.3 (1991), pp. 225-248.
  44. Matthias Baaz, Christian G. Fermüller, and Richard Zach. "Elimination of Cuts in First- Order Finite-Valued Logics". In: Journal of Information Processing and Cybernetics EIK 29.6 (1994), pp. 333-355.
  45. Paolo Baldi and Hykel Hosni. "Depth-bounded Belief functions". In: International Journal of Approximate Reasoning 123 (2020), pp. 26-40.
  46. Alexandru Baltag, Lawrence S. Moss, and Slawomir Solecki. "The logic of public announce- ments, common knowledge, and private suspicions". In: Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge. TARK '98. Evanston, Illinois: Morgan Kaufmann Publishers Inc., 1998, pp. 43-56.
  47. Alexandru Baltag and Sonja Smets. "Conditional Doxastic Models: A Qualitative Approach to Dynamic Belief Revision". In: Electronic Notes in Theoretical Computer Science 165 (2006), pp. 5-21.
  48. Alexandru Baltag et al. "A Topological Approach to Full Belief". In: Journal of Philosoph- ical Logic 48.2 (2019), pp. 205-244. (Visited on 04/20/2023).
  49. J. C. Beall and Greg Restall. Logical Pluralism. Ed. by Greg Restall. Oxford, GB: Oxford University Press, 2005.
  50. Jc Beall. "Free of Detachment: Logic, Rationality, and Gluts". In: Noûs 49.2 (2015), pp. 410-423.
  51. Jc Beall. "The Simple Argument for Subclassical Logic". In: Philosophical Issues 28.1 (2018), pp. 30-54.
  52. Jc Beall and Greg Restall. "Logical Pluralism". In: Australasian Journal of Philosophy 78.4 (2000), pp. 475-493.
  53. Nuel Belnap. "A useful four-valued logic". In: Modern Uses of Multiple-Valued Logic. Ed. by Jon Michael Dunn and George Epstein. Dordrecht: Springer Netherlands, 1977, pp. 5-37.
  54. Nuel Belnap. "Display Logic". In: Journal of Philosophical Logic 11.4 (1982), pp. 375-417.
  55. Nuel Belnap. "How a computer should think". In: Contemporary Aspects of Philosophy. Ed. by Gilbert Ryle. Stocksfield: Oriel Press Ltd., 1977, pp. 30-55.
  56. Joseph Bendana. "Implicit beliefs". In: The Routledge Handbook of Philosophy and Implicit Cognition. Ed. by J Robert Thompson. Routledge, Dec. 2022.
  57. Joseph Bendana and Eric Mandelbaum. "The Fragmentation of Belief". In: ed. by Cristina Borgoni, Dirk Kindermann, and Andrea Onofri. The Fragmented Mind. Oxford: Oxford University Press, Aug. 2021.
  58. Johan van Benthem and Fernando Velázquez-Quesada. "The dynamics of awareness". In: Synthese 177 (2010), pp. 5-27.
  59. Francesco Berto. Topics of Thought. The Logic of Knowledge, Belief, Imagination. Oxford: Oxford University Press, 2022.
  60. Francesco Berto and Mark Jago. Impossible Worlds. Ed. by Mark Jago. Oxford: Oxford University Press, 2019.
  61. Francesco Berto and Greg Restall. "Negation on the Australian Plan". In: Journal of Philo- sophical Logic 48.6 (2019), pp. 1119-1144.
  62. Marta Bílková, Ondrej Majer, and Michal Peliš. "Epistemic logics for sceptical agents". In: Journal of Logic and Computation 26.6 (2016), pp. 1815-1841.
  63. Marta Bílková et al. "Relevant Agents". In: Advances in Modal Logic, Volume 8. Ed. by Lev Beklemishev, Valentin Goranko, and Valentin Shehtman. London: College Publications, 2010, pp. 22-38.
  64. Katalin Bimbó and Jon Michael Dunn. Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi. Center for the Study of Language and Inf, 2008.
  65. Jens Christian Bjerring and Mattias Skipper. "A Dynamic Solution to the Problem of Logical Omniscience". In: Journal of Philosophical Logic 48.3 (2019), pp. 501-521.
  66. Ross T. Brady. "Natural Deduction Systems for Some Quantified Relevant Logics". In: Logique Et Analyse 27.8 (1984), pp. 355-377.
  67. Ross T. Brady. "Relevant Implication and the Case for a Weaker Logic: Dedicated to Robert K. Meyer on the Occasion of His 60th Birthday". In: Journal of Philosophical Logic 25.2 (1996), pp. 151-183.
  68. Ross T. Brady and Andrea Meinander. "Distribution in the Logic of Meaning Containment and in Quantum Mechanics". In: Paraconsistency: Logic and Applications. Ed. by Francesco Berto et al. Springer, 2012, pp. 223-255.
  69. Kai Brünnler. "Deep Sequent Systems for Modal Logic". In: Archive for Mathematical Logic 48.6 (2009), pp. 551-577.
  70. Lewis Carroll. "What the Tortoise Said to Achilles". In: Mind 4.14 (1895), pp. 278-280.
  71. Brian F. Chellas. "Basic Conditional Logic". In: Journal of Philosophical Logic 4.2 (1975), pp. 133-153.
  72. Brian F. Chellas. Modal Logic: An Introduction. Cambridge: Cambridge University Press, 1980.
  73. Alonzo Church. "The Weak Theory of Implication". In: Journal of Symbolic Logic 18.2 (1953), pp. 177-178.
  74. Newton C. A. da Costa. "On the Theory of Inconsistent Formal Systems". In: Notre Dame Journal of Formal Logic 15.4 (1974), pp. 497-510.
  75. Max Cresswell. "Hyperintensional Logic". In: Studia Logica 34.1 (1975), pp. 25-38.
  76. Charles B. Cross and Richmond H. Thomason. "Conditionals and knowledge-base update". In: Belief Revision. Ed. by PeterEditor Gärdenfors. Cambridge Tracts in Theoretical Com- puter Science. Cambridge University Press, 1992, pp. 247-275.
  77. Marcello D'Agostino. "An informational view of classical logic". In: Theoretical Computer Science 606 (2015). Logical and Semantic Frameworks with Applications, pp. 79-97.
  78. Michael De and Hitoshi Omori. "There is More to Negation Than Modality". In: Journal of Philosophical Logic 47.2 (2018), pp. 281-299.
  79. Hans van Ditmarsch, Wiebe van der Hoek, and Barteld Kooi. Dynamic Epistemic Logic. Dordrecht, Netherland: Springer, 2007.
  80. Hans van Ditmarsch, Wiebe van der Hoek, and Barteld Kooi. Dynamic Epistemic Logic. 1st. Springer Publishing Company, Incorporated, 2007.
  81. Kosta Došen. "The First Axiomatization of Relevant Logic". In: Journal of Philosophical Logic 21.4 (1992), pp. 339-356.
  82. Igor Douven. "The Evidential Support Theory of Conditionals". In: Synthese 164.1 (2008), pp. 19-44.
  83. Jon Michael Dunn. "A Comparative Study of Various Model-Theoretic Treatments of Nega- tion: A History of Formal Negation". In: ed. by Dov Gabbay and Heinrich Wansing. Vol. 13. Applied Logic Series. Dordrecht: Springer, Mar. 1999.
  84. Jon Michael Dunn. "Contradictory Information: Too Much of a Good Thing". In: Journal of Philosophical Logic 39.4 (2010), pp. 425-452.
  85. Jon Michael Dunn. "Gentzen system for positive relevant implication". In: Journal of Sym- bolic Logic. Vol. 38. 2. 1973, pp. 356-357.
  86. Jon Michael Dunn. "Intuitive semantics for first-degree entailments and "coupled trees"". In: Philosophical Studies 29.3 (1976), pp. 149-168.
  87. Jon Michael Dunn. "Partiality and Its Dual". In: Studia Logica: An International Journal for Symbolic Logic 66.1 (2000), pp. 5-40.
  88. Jon Michael Dunn. "The Algebra of Intensional Logics". PhD thesis. University of Pitts- burgh, 1966.
  89. Jon Michael Dunn. "The Relevance of Relevance to Relevance Logic". In: Lecture Notes in Computer Science Proceedings ICLA 2015 (Jan. 2015), pp. 11-29.
  90. Jon Michael Dunn and Greg Restall. "Relevance logic". In: Handbook of Philosophical Logic. Ed. by Dov M. Gabbay and Franz Guenthner. 2nd. Vol. 6. Kluwer, 2002, pp. 1-128.
  91. Jon Michael Dunn and Chunlai Zhou. "Negation in the Context of Gaggle Theory". In: Studia Logica: An International Journal for Symbolic Logic 80.2/3 (2005), pp. 235-264.
  92. Jeremy Seligman Edwin D. Mares and Greg Restall. "Situations, Constraints and Chan- nels". In: Handbook of Logic and Language. Ed. by Alice ter Meulen Johan van Benthem. Cambridge: North Holland, 1997, pp. 329-344.
  93. Ronald Fagin and Joseph Y. Halpern. "Belief, awareness, and limited reasoning". In: Ar- tificial Intelligence 34.1 (1987), pp. 39-76.
  94. Ronald Fagin, Joseph Y. Halpern, and Moshe Vardi. "A nonstandard approach to the logical omniscience problem". In: Artificial Intelligence 79 (1995), pp. 203-240.
  95. Federico L. G. Faroldi. "Deontic Modals and Hyperintensionality". In: Logic Journal of the IGPL 27.4 (2019), pp. 387-410.
  96. Nicholas Ferenz. "First-Order Relevant Reasoners in Classical Worlds". In: The Review of Symbolic Logic (2023), pp. 1-26.
  97. Nicholas Ferenz and Andrew Tedder. "Neighbourhood Semantics for Modal Relevant Log- ics". In: Journal of Philosophical Logic 52.1 (2023), pp. 145-181.
  98. Thomas Macaulay Ferguson. "A Computational Interpretation of Conceptivism". In: Jour- nal of Applied Non-Classical Logics 24.4 (2014), pp. 333-367.
  99. Thomas Macaulay Ferguson. "Faulty Belnap Computers and Subsystems of Fde". In: Jour- nal of Logic and Computation 26.5 (2016), pp. 1617-1636.
  100. Thomas Macaulay Ferguson. "Subject-matter and intensional operators I: Conditional- agnostic analytic implication". In: Philosophical Studies 180 (7 2023), pp. 1849-1879.
  101. Thomas Macaulay Ferguson. "Subject-Matter and Intensional Operators II: Applications to the Theory of Topic-Sensitive Intentional Modals". In: Journal of Philosophical Logic 52.6 (2023), pp. 1673-1701.
  102. Thomas Macaulay Ferguson and Shay Allen Logan. "Topic Transparency and Variable Sharing in Weak Relevant Logics". In: Erkenntnis (2024), pp. 1-28.
  103. Eduardo Fermé and Sven Ove Hansson. "AGM 25 Years: Twenty-Five Years of Research in Belief Change". In: Journal of Philosophical Logic 40 (Apr. 2011), pp. 295-331.
  104. Eduardo Fermé and Sven Ove Hansson. Belief Change: Introduction and Overview. Springer Verlag, 2018.
  105. Kit Fine. "Analytic Implication". In: Notre Dame Journal of Formal Logic 27.2 (1986), pp. 169-179.
  106. Kit Fine. "Models for Entailment". In: Journal of Philosophical Logic 3.4 (1974), pp. 347- 372.
  107. Andre Fuhrmann. "Relevant Logics, Modal Logics and Theory Change". PhD Thesis. Aus- tralian National University, 1988.
  108. Dov Gabbay, Odinaldo Rodrigues, and Alessandra Russo. "Belief Revision in Non-Classical logics". In: The Review of Symbolic Logic 1.3 (2008), pp. 267-304.
  109. Ying Gao and Jingde Cheng. "Semantics for a Basic Relevant Logic with Intensional Conjunction and Disjunction". In: Electronic Notes in Theoretical Computer Science 169 (2007). Proceedings of the Workshop on Logic, Models and Computer Science (LMCS 2006), pp. 61-71.
  110. Peter Gärdenfors. "Belief Revisions and the Ramsey Test for Conditionals". In: The Philo- sophical Review 95.1 (1986), pp. 81-93.
  111. Gerhard Gentzen. "Investigations Into Logical Deduction". In: American Philosophical Quarterly 1.4 (1964), pp. 288-306.
  112. Gerhard Gentzen. "Untersuchungen über das logische Schließen I". In: Mathematische Zeitschrift 39 (1935), pp. 176-210.
  113. Jelle Gerbrandy and Willem Groeneveld. "Reasoning About Information Change". In: Journal of Logic, Language and Information 6.2 (1997), pp. 147-169.
  114. Jean-Yves Girard. "Linear logic". In: Theoretical Computer Science 50.1 (1987), pp. 1-101.
  115. Lou Goble. "A Logic for Deontic Dilemmas". In: Journal of Applied Logic 3.3-4 (2005), pp. 461-483.
  116. Lou Goble. "Neighborhoods for Entailment". In: Journal of Philosophical Logic 32.5 (2003), pp. 483-529.
  117. Nelson Goodman. "Fact, Fiction, and Forecast". In: Philosophy 31.118 (1955), pp. 268-269.
  118. Andrzej Grzegorczyk. "A philosophically plausible formal interpretation of intuitionistic logic". In: Indagationes Mathematicae 26.5 (1964), pp. 596-601.
  119. Susan Haack. Philosophy of Logics. London and New York: Cambridge University Press, 1978.
  120. Joseph Halpern. "Alternative Semantics for Unawareness". In: Games and Economic Be- havior 37 (May 2000), pp. 321-339.
  121. Gilbert Harman. Change in View: Principles of Reasoning. Cambridge, MA, USA: MIT Press, 1986.
  122. Gilbert Harman. "Logic and Reasoning". In: Synthese 60.1 (1984), pp. 107-127.
  123. Peter Hawke, Aybüke Özgün, and Francesco Berto. "The Fundamental Problem of Logical Omniscience". In: Journal of Philosophical Logic (2020).
  124. Jaakko Hintikka. "Impossible Possible Worlds Vindicated". In: Journal of Philosophical Logic 4.4 (1975), pp. 475-484.
  125. Jaakko Hintikka. Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca, N.Y., Cornell University Press, 1962.
  126. Ole Thomassen Hjortland. "Logical Pluralism, Meaning-Variance, and VerbalDisputes". In: Australasian Journal of Philosophy 91.2 (2013), pp. 355-373.
  127. Wesley H. Holliday. "A Fundamental Non-Classical Logic". In: logics (2023).
  128. Wesley H. Holliday. "Epistemic Logic and Epistemology". In: Handbook of Formal Philos- ophy. Ed. by Sven Ove Hansson Vincent F. Hendricks. Springer, 2018, pp. 351-369.
  129. Wesley H. Holliday and Matthew Mandelkern. "The Orthologic of Epistemic Modals". In: Journal of Philosophical Logic 53.4 (2024), pp. 831-907.
  130. Levin Hornischer. "Logics of Synonymy". In: Journal of Philosophical Logic 49.4 (2020), pp. 767-805.
  131. Luca Incurvati and Julian J. Schlöder. "Weak Rejection". In: Australasian Journal of Phi- losophy 95.4 (2017), pp. 741-760.
  132. Lawrence S. Moss Jeremy Seligman. "Situation theory". In: Handbook of Logic and Lan- guage. Ed. by Alice ter Meulen Johan van Benthem. Cambridge: North Holland, 1997, pp. 253-328.
  133. Sonja Smets Johan van Benthem. "Dynamic Logics of Belief Change". English. In: Hand- book of Epistemic Logic. Ed. by Hans van Ditmarsch et al. College Publications, 2015, pp. 313-393.
  134. Hirofumi Katsuno and Alberto O. Mendelzon. "On the Difference Between Updating a Knowledge Base and Revising It". In: Belief Revision. Ed. by H. Katsuno and A. O. Mendelzon. Cambridge University Press, 1992, pp. 183-203.
  135. Stephen Cole Kleene. Introduction to Metamathematics. Groningen: P. Noordhoff N.V., 1952.
  136. Kurt Konolige. A Deduction Model of Belief. Los Atlos, Calif.: Morgan Kaufmann Publish- ers, 1986.
  137. Barteld Kooi and Bryan Renne. "Arrow Update Logic". In: The Review of Symbolic Logic 4.4 (2011), pp. 536-559.
  138. Angelika Kratzer. "Conditionals". In: Semantics: An International Handbook of Contem- porary Research. Ed. by A. von Stechow and D. Wunderlich. Berlin: Walter de Gruyter, 1991, pp. 651-656.
  139. Sarit Kraus, Daniel Lehmann, and Menachem Magidor. "Nonmonotonic reasoning, prefer- ential models and cumulative logics". In: Artificial Intelligence 44.1 (1990), pp. 167-207.
  140. Saul Kripke. "Semantical Analysis of Modal Logic II: Non-Normal Modal Propositional Calculi". In: Symposium on the Theory of Models. Ed. by J.W. Addison, L. Henkin, and A. Tarski. Amsterdam: North-Holland, 1965, pp. 206-221.
  141. Saul Kripke. "Semantical Considerations on Modal Logic". In: Acta Philosophica Fennica 16 (1963), pp. 83-94.
  142. Gerhard Lakemeyer. "Tractable Meta-Reasoning in Propositional Logics of Belief." In: IJCAI 1987. 1987, pp. 401-408.
  143. Gerhard Lakemeyer and Wilfried Lang. "Belief revision in a nonclassical logic". In: KI-96: Advances in Artificial Intelligence. Ed. by Günther Görz and Steffen Hölldobler. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996, pp. 199-211.
  144. Joachim Lambek. "Deductive systems and categories II. Standard constructions and closed categories". In: Category Theory, Homology Theory and their Applications I. Ed. by Peter J. Hilton. Berlin, Heidelberg: Springer Berlin Heidelberg, 1969, pp. 76-122.
  145. Hannes Leitgeb. "HYPE: A System of Hyperintensional Logic". In: Journal of Philosophical Logic 48.2 (2019), pp. 305-405.
  146. Hannes Leitgeb. "On the Ramsey Test Without Triviality". In: Notre Dame Journal of Formal Logic 51.1 (2010), pp. 21-54.
  147. Hector J. Levesque. "A logic of implicit and explicit belief". In: Proceedings of AAAI 1984. 1984, pp. 198-202.
  148. Hector J. Levesque and Gerhard Lakemeyer. The Logic of Knowledge Bases. MIT Press, 2001.
  149. Clarence Irving Lewis. "Implication and the Algebra of Logic". In: Mind 21.84 (1912), pp. 522-531.
  150. Clarence Irving Lewis and Cooper Harold Langford. Symbolic Logic. 2nd. Dover Publica- tions, 1959.
  151. David K. Lewis. Counterfactuals. Malden, Mass.: Blackwell, 1973.
  152. David K. Lewis. "General Semantics". In: Synthese 22.1-2 (1970), pp. 18-67.
  153. Shay Allen Logan. Relevance Logic. New York, NY, USA: Cambridge University Press, 2024.
  154. David Makinson. Bridges From Classical to Nonmonotonic Logic. London: College Publi- cations, 2005.
  155. Edwin D. Mares. "A Paraconsistent Theory of Belief Revision". In: Erkenntnis 56.2 (2002), pp. 229-246.
  156. Edwin D. Mares. Relevant Logic: A Philosophical Interpretation. Cambridge University Press, 2004.
  157. Edwin D. Mares and André Fuhrmann. "A Relevant Theory of Conditionals". In: Journal of Philosophical Logic 24.6 (1995), pp. 645-665.
  158. John Jules Meyer and Wiebe Van Der Hoek. Epistemic Logic for AI and Computer Science. Cambridge University Press, 1995.
  159. Robert K. Meyer and Edwin D. Mares. "Semantics of Entailment 0". In: Substructural Logics. Ed. by Peter Schroeder-Heister and Kosta Dosen. Oxford Science Publications, 1993, pp. 239-258.
  160. Robert K. Meyer and Richard Routley. "Algebraic Analysis of Entailment I". In: Logique et Analyse 15.59/60 (1972), pp. 407-428.
  161. Grigori Mints. "Cut-elimination theorem for relevant logics". In: Journal of Soviet Mathe- matics 6.4 (1976), pp. 422-428.
  162. Salvatore Modica and Aldo Rustichini. "Unawareness and Partitional Information Struc- tures". In: Games and Economic Behavior 27.2 (1999), pp. 265-298.
  163. Shaw-Kwei Moh. "The Deduction Theorems and Two New Logical Systems". In: Journal of Symbolic Logic 17.2 (1952), pp. 153-154.
  164. Lawrence Moss. "Dynamic Epistemic Logic". English. In: Handbook of Epistemic Logic. Ed. by Hans van Ditmarsch et al. College Publications, 2015, pp. 261-312.
  165. Sergei Odintsov and Heinrich Wansing. "Routley Star and Hyperintensionality". In: Journal of Philosophical Logic 50.1 (2020), pp. 33-56.
  166. Hitoshi Omori and Michael De. "Shrieking, Shrugging, and the Australian Plan". In: Notre Dame Journal of Formal Logic 63.2 (2022), pp. 137-141.
  167. Hitoshi Omori and Katsuhiko Sano. "Generalizing Functional Completeness in Belnap- Dunn Logic". In: Studia Logica: An International Journal for Symbolic Logic 103.5 (2015), pp. 883-917.
  168. Hitoshi Omori and Heinrich Wansing. "40 years of FDE: An introductory overview". In: Studia Logica 105.6 (2017), pp. 1021-1049.
  169. I. E. Orlov. "The Calculus of Compatibility of Propositions (in Russian)". In: Mathematics of the USSR. Sbornik (Matematicheskii Sbornik) 35 (1928), pp. 263-286.
  170. Aybüke Özgün and Francesco Berto. "Dynamic Hyperintensional Belief Revision". In: The Review of Symbolic Logic 14.3 (2021), pp. 766-811.
  171. Eric Pacuit. Neighborhood Semantics for Modal Logic. Dordrecht: Springer, Jan. 2017.
  172. Francesco Paoli. "Implicational Paradoxes and the Meaning of Logical Constants". In: Australasian Journal of Philosophy 85.4 (2007), pp. 553-579.
  173. William T. Parry. "Analytic Implication; Its History, Justification and Varietiess". In: Directions in Relevant Logic. Ed. by Jean Norman and Richard Sylvan. Dordrecht: Springer Netherlands, 1989, pp. 101-118.
  174. William T. Parry. "Ein Axiomensystem für eine neue Art von Implikation (analytische Implikation)". In: Ergebnisse eines mathematischen Kolloquiums. Vol. 4. 1933, pp. 5-6.
  175. Jan Plaza. "Logics of Public Communications". In: Synthese 158.2 (2007), pp. 165-179.
  176. Francesca Poggiolesi. "The Method of Tree-Hypersequents for Modal Propositional Logic". In: Towards Mathematical Philosophy: Papers from the Studia Logica conference Trends in Logic IV. Ed. by David Makinson, Jacek Malinowski, and Heinrich Wansing. Dordrecht: Springer Netherlands, 2009, pp. 31-51.
  177. Adam Prenosil. "Reasoning with inconsistent information". PhD thesis. Ph. D. Thesis, Charles University, 2018.
  178. Graham Priest. Doubt Truth to Be a Liar. New York: Oxford University Press, 2006.
  179. Graham Priest. In Contradiction: A Study of the Transconsistent. New York: Oxford Uni- versity Press, 2006.
  180. Graham Priest. "Paraconsistent Belief Revision". In: Theoria 67.3 (2001), pp. 214-228.
  181. Graham Priest. "The Logic of Paradox". In: Journal of Philosophical Logic 8.1 (1979), pp. 219-241.
  182. Graham Priest. "The Logic of the Catuskoti". In: Comparative Philosophy 1.2 (2010), pp. 24-54.
  183. Graham Priest. Towards non-being. Oxford University Press, 2016.
  184. Vít Puncochář, Igor Sedlár, and Andrew Tedder. "Relevant epistemic logic with public announcements and common knowledge". In: Journal of Logic and Computation 33.2 (Jan. 2023), pp. 436-461.
  185. Vít Punčochář and Igor Sedlár. "Substructural Logics for Pooling Information". In: Logic, Rationality, and Interaction. Ed. by Alexandru Baltag, Jeremy Seligman, and Tomoyuki Yamada. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017, pp. 407-421.
  186. Frank Plumpton Ramsey. "General Propositions and Causality". In: The Foundations of Mathematics and other Logical Essays. Ed. by Frank Plumpton Ramsey. Kegan Paul, Trench, Trübner, 1929, pp. 237-255.
  187. Veikko Rantala. "Impossible worlds semantics and logical omniscience". In: Acta Philo- sophica Fennica 35 (1982), pp. 106-115.
  188. Stephen Read. Relevant Logic: A Philosophical Examination of Inference. Oxford: Black- well, 1988.
  189. Greg Restall. An Introduction to Substrucutral Logics. London: Routledge, 2000.
  190. Greg Restall. "Displaying and Deciding Substructural Logics 1: Logics with Contraposi- tion". In: Journal of Philosophical Logic 27.2 (1998), pp. 179-216.
  191. Greg Restall. "Information Flow and Relevant Logics". In: Logic, Language and Compu- tation. Ed. by Jerry Seligman and Dag Westerstahl. CSLI Publications, Stanford, 1996, pp. 463-477.
  192. Greg Restall. "Relevant and Substructural Logics". In: Handbook of the History of Logic. Ed. by Dov Gabbay and John Woods. Vol. 7. Elsevier, Sept. 2006, pp. 289-398.
  193. David Ripley. "Negation in Natural Language". PhD thesis. University of North Car- olina/Chapel Hill, 2009.
  194. Hans Rott. "Difference-Making Conditionals and the Relevant Ramsey Test". In: The Re- view of Symbolic Logic 15.1 (2022), pp. 133-164.
  195. Richard Routley. "Ultralogic as universal? by Richard Routley". In: Ultralogic as Univer- sal? The Sylvan Jungle -Volume 4. Ed. by Zach Weber. Cham: Springer International Publishing, 2019, pp. 1-121.
  196. Richard Routley and Robert K. Meyer. "The Semantics of Entailment". In: Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Ed. by Hugues Leblanc. North-Holland Publishing Company, 1973, pp. 199-243.
  197. Richard Routley and Robert K. Meyer. "The Semantics of Entailment -III". In: Journal of Philosophical Logic 1.2 (1972), pp. 192-208.
  198. Richard Routley and Robert K. Meyer. "The Semantics of Entailment II". In: Journal of Philosophical Logic 1.1 (1972), pp. 53-73.
  199. Richard Routley and Robert K. Meyer. "Towards a general semantical theory of implication and conditionals. I. Systems with normal conjunctions and disjunctions and aberrant and normal negations". In: Reports on Mathematical Logic 4 (1975), pp. 67-89.
  200. Richard Routley and Robert K. Meyer. "Towards a general semantical theory of implication and conditionals. II. Improved negation theory and propositional identity". In: Reports on Mathematical Logic 9 (1976), pp. 47-62.
  201. Richard Routley and Valerie Routley. "The Semantics of First Degree Entailment". In: Noûs 6.4 (1972), pp. 335-359.
  202. Richard Routley et al. Relevant Logics and Their Rivals. Vol. 1. Ridgeview, 1982.
  203. Burkhard Schipper. "Awareness". English. In: Handbook of Epistemic Logic. Ed. by Hans van Ditmarsch et al. College Publications, 2015, pp. 77-146.
  204. Igor Sedlár. "Algebras for Relevant Reasoners". In: Journal of Applied Logics -IfCoLog Journal (Forthcoming).
  205. Igor Sedlár. "Epistemic extensions of modal distributive substructural logics". In: Journal of Logic and Computation 26.6 (2016), pp. 1787-1813.
  206. Igor Sedlár. "Hyperintensional Logics for Everyone". In: Synthese 198.2 (2019), pp. 933- 956.
  207. Igor Sedlár. "Substructural epistemic logics". In: Journal of Applied Non-Classical Logics 25.3 (2015), pp. 256-285.
  208. Igor Sedlár and Andrew Tedder. "Situated Epistemic Updates". In: Proceedings of Logic, Rationality, and Interaction 2021. Ed. by Sujata Ghosh and Thomas Icard. Springer Verlag, 2021, pp. 192-200.
  209. Igor Sedlár and Pietro Vigiani. "Epistemic Logics for Relevant Reasoners". In: Journal of Philosophical Logic 53 (2024), pp. 1383-1411.
  210. Igor Sedlár and Pietro Vigiani. "Explicit and Implicit Belief in First Degree Entailment With Strict Implication". In: New Directions in Relevant Logic. Ed. by Andrew Tedder Igor Sedlár and Shawn Standafer. Dordrecht: Springer Netherlands, 2025, pp. 425-452.
  211. Igor Sedlár and Pietro Vigiani. "Relevant Reasoners in a Classical World". In: Advances in Modal Logic, Volume 14. Ed. by David Fernández Duque, Alessandra Palmigiano, and Sophie Pichinat. London: College Publications, 2022, pp. 697-718.
  212. Igor Sedlár and Pietro Vigiani. "Relevant Reasoning and Implicit Beliefs". In: Logic, Lan- guage, Information, and Computation. Ed. by Helle Hvid Hansen, Andre Scedrov, and Ruy J.G.B. de Queiroz. Cham: Springer Nature Switzerland, 2023, pp. 336-350.
  213. Krister Segerberg. "Notes on Conditional Logic". In: Studia Logica 48.2 (1989), pp. 157- 168.
  214. Takahiro Seki. "A Sahlqvist Theorem for Relevant Modal Logics". In: Studia Logica 73.3 (Apr. 2003), pp. 383-411.
  215. Takahiro Seki. "General frames for relevant modal logics". In: Notre Dame Journal of Formal Logic 44.2 (2003), pp. 93-109.
  216. Sebastian Sequoiah-Grayson. "A Logic of Affordances". In: The Logica Yearbook 2020. Ed. by M. Blicha and I. Sedlár. 2021, pp. 219-236.
  217. Sebastian Sequoiah-Grayson. "Dynamic Negation and Negative Information". In: The Re- view of Symbolic Logic 2.1 (2009), pp. 233-248.
  218. Sebastian Sequoiah-Grayson. "Epistemic Closure and Commutative, Nonassociative Resid- uated Structures". In: Synthese 190.1 (2013), pp. 113-128.
  219. Sebastian Sequoiah-Grayson. "Epistemic Relevance and Epistemic Actions". In: J. Michael Dunn on Information Based Logics. Ed. by Katalin Bimbó. Cham: Springer International Publishing, 2016, pp. 133-146.
  220. Yaroslav Shramko. "Hilbert-style axiomatization of first-degree entailment and a family of its extensions". In: Annals of Pure and Applied Logic 172.9 (2021).
  221. Sonja Smets and Alexandru Baltag. "A semantic-modal view on Ramsey's test". English. In: LogKCA10. Proceedings of the second ILCLI international workshop on logic and philos- ophy of knowledge, communication and action. Ed. by X. Arrazola and M. Ponte. University of the Basque country press, 2010, pp. 119-134.
  222. Anthia Solaki, Francesco Berto, and Sonja Smets. "The Logic of Fast and Slow Thinking". In: Erkenntnis 86.3 (2021), pp. 733-762.
  223. Robert Stalnaker. "A note on non-monotonic modal logic". In: Artificial Intelligence 64.2 (1993), pp. 183-196.
  224. Robert Stalnaker. "A Theory of Conditionals". In: Studies in Logical Theory. Ed. by Nicholas Rescher. Blackwell, 1968, pp. 98-112.
  225. Robert Stalnaker. "On Logics of Knowledge and Belief". In: Philosophical Studies 128.1 (2006), pp. 169-199.
  226. Robert Stalnaker. "The Problem of Logical Omniscience, I". In: Synthese 89.3 (1991), pp. 425-440.
  227. Shawn Standefer. "Hyperintensionality in Relevant Logics". In: Logic, Rationality, and Interaction: 9th International Workshop, LORI 2023, Jinan, China, October 26-29, 2023, Proceedings. Ed. by Natasha Alechina, Andreas Herzig, and Fei Liang. Springer Nature Switzerland, 2023, pp. 238-250.
  228. Shawn Standefer. "Routes to relevance: Philosophies of relevant logics". In: Philosophy Compass 19.2 (2024), e12965.
  229. Shawn Standefer. "Tracking reasons with extensions of relevant logics". In: Logic Journal of the IGPL 27.4 (June 2019), pp. 543-569.
  230. Shawn Standefer. "What is a Relevant Connective?" In: Journal of Philosophical Logic 51.4 (2022), pp. 919-950.
  231. Shawn Standefer, Ted Shear, and Rohan French. "Getting Some (Non-Classical) Closure with Justification Logic". In: Asian Journal of Philosophy 2.2 (2023), pp. 1-25.
  232. Richard Sylvan. "Relevant Containment Logics and Certain Frame Problems of AI". In: Logique Et Analyse 31 (1988), pp. 11-25.
  233. Andrew Tedder. "Topics in Relevant Logic: A Semantic Perspective". In: Erkenntnis (2024), pp. 1-29.
  234. Andrew Tedder and Marta Bilková. "Relevant Propositional Dynamic Logic". In: Synthese 200.3 (2022), pp. 1-42.
  235. Andrew Tedder and Nicholas Ferenz. "Neighbourhood Semantics for Quantified Relevant Logics". In: Journal of Philosophical Logic 51.3 (2022), pp. 457-484.
  236. Matthias Unterhuber and Gerhard Schurz. "Completeness and Correspondence in Chellas- Segerberg Semantics". In: Studia Logica 102.4 (2014), pp. 891-911.
  237. Alasdair Urquhart. "Semantics for Relevant Logics". In: The Journal of Symbolic Logic 37.1 (1972), pp. 159-169.
  238. Fernando Velazquez-Quesada. "Dynamic Epistemic Logic for Implicit and Explicit Beliefs". In: Journal of Logic Language and Information 23 (2014), pp. 107-140.
  239. Fernando Velázquez-Quesada. "Explicit and Implicit Knowledge in Neighbourhood Mod- els". In: Proceedings of the 4th International Workshop on Logic, Rationality, and Inter- action -Volume 8196. LORI 2013. Hangzhou, China: Springer-Verlag, 2013, pp. 239-252. isbn: 9783642409479.
  240. Pietro Vigiani. "A Hyperintensional Logic of Non-prime Evidence". In: Journal of Philo- sophical Logic 53.3 (2024), pp. 761-788.
  241. Pietro Vigiani. "Conditional Logic with Relevant Updates". In: (Under review).
  242. Pietro Vigiani. "Relevant Epistemic Logic with State-Sensitive Topics". In: Synthese 205.35 (2025), pp. 1-28.
  243. Pietro Vigiani and Thomas Macaulay Ferguson. Contextual Entailment and Containment: A Ternary Approach to Information and Topic Inclusion. Under review.
  244. Heinrich Wansing. "A general possible worlds framework for reasoning about knowledge and belief". In: Studia Logica 49.4 (1990), pp. 523-539.
  245. Heinrich Wansing. "On Split Negation, Strong Negation, Information, Falsification, and Verification". In: J. Michael Dunn on Information Based Logics. Ed. by Katalin Bimbó. Cham: Springer International Publishing, 2016, pp. 161-189.
  246. Timothy Williamson. "Indicative versus Subjunctive Conditionals, Congruential versus Non-Hyperintensional Contexts". In: Philosophical Issues 16 (2006), pp. 310-333.
  247. Deirdre Wilson and Dan Sperber. "Relevance Theory". In: The Handbook of Pragmatics. Ed. by L. Horn and G. Ward. Blackwell, 2002, pp. 607-632.
  248. Stephen Yablo. Aboutness. Oxford: Princeton University Press, 2014.

Related papers

Non-classical modal logic for belief
Michael McPartlin

1991

of Thesis The standard model of knowledge and belief attributes to agents the ability to reason perfectly in classical logic. This is known as the problem of logical omniscience and, in accordance with the requirements of their contexts of use, has led to the development of a number of alternative epistemic logics. Some of these alternatives can, like the standard model, be regarded as presenting for discussion and analysis in a base language a system of reasoning, or consequence relation: the relation under which beliefs are closed. Adopting this perspective with regard to a useful four-valued logic, the resulting extension of the standard model is described and many technical points of comparison with the original model are given.

View PDFchevron_right
Issues in epistemic and modal logics and their applications
Cezar Mortari

1991

Under "epistemic-doxastic logic"-EDL for short-we undersland a logic system in which both concepLs, knowledge and belief, are contemplated.) So, to begin this work, and to set its main and more importam goal, I will follow their suggestion an d try to characterize "minimal epistemic statcs" in different EDL-calculi. In other words, I'll be looking for ways of describing Angela's epistemic (i.e., knowledge or belief-we'll decide it laler) stale under lhe supposition that she knows or believes only some formula a. In doing this I won't stay resiricted to the only EDL-system proposed by HM (since this logic's "knowledge branch" is S5, and I am not lhat convinced that S5 is lhe best option in formalizing knowledge), but 1*11 ralher try to work with several calculi of different strength. Thus, in Chapter I, we ll have an overview of some epistemic-doxastic logics. I will introduce several systems which we'll be working with, giving for each one an axiomatic presentalion. This will be accompanied by a small discussion about lhe tenability of the various epistemic-doxastical principies involved. Also in the syntactical part are includcd some results about lhe number of modalilies and the

View PDFchevron_right
Modal negation in epistemic logic
Igor Sedlar

The article adds a negative modal operator ~ to normal modal epistemic logics. ~A is seen as representing the set of propositions taken as sufficient grounds to refute A within a specific epistemic context. An operator of contextual belief is defined in terms of ruling out ~A. A number of epistemic logics with different variants of modal negation are explored. It is shown that, in most of the logics, contextual belief avoids the logical omniscience problem. It is also shown that using modal negation in public announcement logic yields a specific form of non-monotonic information update, related to changes of epistemic context. Two variants of modal negation are linked to the Relevant Alternatives theory of knowledge and to abstract argumentation frameworks. The technical results include complete axiomatizations of a number of epistemic logics with modal negation and a proof or a reduction schema for ~ within public announcement logic.

View PDFchevron_right
A simple modal logic for belief revision : Extended Abstract
Giacomo Bonanno

2005

The notions of static belief and of belief revision have been extensively studied in the literature. However, there is a surprising lack of uniformity in the two approaches. In the philosophy and logic literature the notion of static belief has been studied mainly within the context of modal logic. On the syntactic side a belief operator B is introduced, with the intended interpretation of B as “the individual believes that ”. Various properties of beliefs are then expressed by means of axioms, such as the positive introspection axiom B ! BB , which says that if the individual believes then she believes that she believes . On the semantic side Kripke structures are used, consisting of a set of states (or possible worlds) together with a binary relation B on , with the interpretation of B as “at state the individual considers state possible”. The connection between syntax and semantics is then obtained by means of a valuation V which associates with every atomic sentence p the set of...

View PDFchevron_right
An investigation of modal structures as an alternative semantic basis for epistemic logics
James Delgrande

Computational Intelligence, 1989

In the past, Kripke structures have been used to specify the semantic theory of various modal logics. More recently, modal structures have been developed as an alternative to Kripke structures for providing the semantics of such logics. While these approaches are equivalent in a certain sense, it has been argued that modal structures provide a more appropriate basis for representing the modal notions of knowledge and belief. Since these notions, rather than the traditional notions of necessity and possibility, are of particular interest to artificial intelligence, it is of interest to examine the applicability and versatility of these structures. This paper presents an investigation of modal structures by examining how they may be extended to account for generalizations of Kripke structures. To begin with, we present an alternative formulation of modal structures in terms of trees; this formulation emphasizes the relation between Kripke structures and modal structures, by showing how the latter may be obtained from the former by means of a three-step transformation. Following this, we show how modal structures may be extended to represent generalizations of possible worlds, and to represent generalizations of accessibility between possible worlds. Lastly, we show how modal structures may be used in the case of a full first-order system. In all cases, the extensions are shown to be equivalent to the corresponding extension of Kripke structures.

View PDFchevron_right
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved