Academia.eduAcademia.edu

Outline

Title
Abstract
Introduction 1.ABDUCTIVE Reasoning
Abductive Inference and the Material Conditional
Related Work
References

A Conditional Logic of Abduction

Profile image of Atocha AlisedaAtocha Aliseda

Publication Name: Synthese (forthcoming; DOI: 10.1007/s11229-014-0496-0)

Abstract

""A Conditional Logic for Abduction We propose a logic of abduction that (i) provides an appropriate formalization of the explanatory conditional, and that (ii) captures the defeasible nature of abductive inference. For (i), we argue that explanatory conditionals are non-classical, and rely on Brian Chellas’s work on conditional logics for providing an alternative formalization of the explanatory conditional. For (ii), we make use of the adaptive logics framework for modeling defeasible reasoning. We show how our proposal allows for a more natural reading of explanatory relations, and how it overcomes problems faced by other systems in the literature. ""

Related papers

The Role of Abduction in Logic Programming
Antonis Kakas

Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 5: Logic Programming, 1998

This paper extends and updates our earlier survey and analysis of work on the extension of logic programming to perform abductive reasoning [Kakas et al., 1993]. The purpose of the paper is to provide a critical overview of some of the main research results, in order to develop a common framework for evaluating these results, to identify the main unresolved problems, and to indicate directions for future work. The emphasis is not on technical details but on relationships and common features of different approaches. Some of the main issues we will consider are the contributions that abduction can make to the problems of reasoning with incomplete or negative information, the evolution of knowledge, and the semantics of logic programming and its extensions. We also discuss recent work on the argumentation-theoretic interpretation of abduction, which was introduced in the earlier version of this paper. The philosopher Peirce first introduced the notion of abduction. In [Peirce, 1931-58]...

View PDFchevron_right
Abduction and Abductive Logic Programming
Paolo Mancarella
View PDFchevron_right
The Role of Abduction in Logic Programming A.C. Kakas
Antonis Kakas

This paper is a survey and critical overview of recent work on the extension of Logic Programming to perform Abductive Reasoning (Abductive Logic Programming). It updates the earlier paper \Abductive Logic Programming" 88]. We outline the general framework of Abduction and its applications to Knowledge Assimilation and Default Reasoning; we describe the argumentation-theoretic approach to the use of abduction as an interpretation for Negation as Failure, introduced in the earlier version 88] of this paper; and we present recent work on the generalisation of the argumentation-theoretic approach to provide a framework for default reasoning in general. We also analyse the links between Abduction and Constraint Logic Programming, as well as between Abduction and the extension of Logic Programming obtained by adding a form of explicit negation. Finally we discuss the relation between Abduction and Truth Maintenance.

View PDFchevron_right
A first approach to abductive defeasible logic programming: formalization and properties
Guillermo R Simari

2007

This article presents the confluence of two general ideas: Defeasible Logic Programming (DeLP, an argumentation based formalism for representing knowledge and reasoning) and Abduction in logic. In first place, we introduce a framework that formally states the problem of doing abduction (obtaining abductive explanations) in the particular case that the abductive theory is a DeLP Program. In the reminder of this work we face that problem, providing a formal characterization of the notion of abductive explanation, in such a way that we could then easily calculate the explanations from this formal characterization. An important advantage of this approach is that by proving the correctness of the characterization, we ensure the correctness of the method for obtaining explanations.

View PDFchevron_right
A unified model for abduction-based reasoning
Shengrui Wang

IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 1998

View PDFchevron_right
Logic and Abduction
Lorenzo Magnani

Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia, 2008

ABSTRACT: In her book Abductive Reasoning Atocha Aliseda (2006) stresses the attention to the logical models of abduction, centering on the semantic tableaux as a method for extending and improving both the whole cognitive/philosophical view on it and on other more restricted logical approaches. I will provide further insight on two aspects. The first is related to the importance of increasing logical knowledge on abduction: Aliseda clearly shows how the logical study on abduction in turn helps us to extend and modernize the ...

View PDFchevron_right
Dynamical Logic Driven by Classified Inferences Including Abduction
Koji Sawa

2010

We propose a dynamical model of formal logic which realizes a representation of logical inferences, deduction and induction. In addition, it also represents abduction which is classified by Peirce as the third inference following deduction and induction. The three types of inference are represented as transformations of a directed graph. The state of a relation between objects of the model fluctuates between the collective and the distinctive. In addition, the location of the relation in the sequence of the relation influences its state.

View PDFchevron_right
L. Magnani, Naturalizing the logic of abduction Logic Journal of IGPL
Lorenzo Magnani

There never was a sounder logical maxim of scientific procedure than Ockham's razor: Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well. No matter if it takes fifty generations of arduous experimentation to explode the simpler hypothesis, and no matter how incredible it may seem that that simpler hypothesis should suffice, still fifty generations are nothing in the life of science, which has all time before it …. But you will mark the limitation of my approval of Ockham's razor. It is a sound maxim of scientific procedure. If the question be what one ought to believe, the logic of the situation must take other factors into account. Charles Sanders Peirce, Harvard Lectures on Pragmatism, Lecture II, 1903. Abstract I will analyse some properties of abduction that are essential from a logical standpoint. When dealing with the so-called 'inferential problem', I will opt for the more general concepts of input and output instead of those of premisses and conclusions, and show that in this framework two consequences can be derived that help clarify basic logical aspects of abductive reasoning: (i) it is more natural to accept the 'multimodal' and 'context-dependent' character of the inferences involved, (ii) inferences are not merely conceived of in the terms of the process leading to the 'generation of an output' or to the proof of it, as in the traditional and standard view of deductive proofs, but rather, from this perspective abductive inferences can be seen as related to logical processes in which input and output fail to hold each other in an expected relation, with the solution involving the modification of inputs, not that of outputs. I will also describe that if we wish to naturalize the logic of the abductive processes and its special consequence relation, we should refer to the following main aspects: 'optimization of situatedness', 'maximization of changeability' of both input and output, and high 'information-sensitiveness'. 1 Abductive Inferences: Input and Output vs. Premisses and Conclusions From the perspective of the EC-Model of abduction, 1 the available logical views concerning abduction have to be reconsidered. By now this fact is acknowledged by some logicians. Estrada-González [10, p. 182], e.g. by referring to the properties called consistency, minimality, etc. stated in the AKM-schema 2 usefully notes: We think that overemphasizing the characteristics of abduction as it occurs in scientific practices and daily life scenarios has led to overlook some features that abduction in those circumstances shares with other phenomena in which some given outputs fail to stand in a certain relation with some given inputs and thus a modification on those inputs is in order. Indeed, abduction in an eco-cognitive perspective is not circumscribed by indicating particular requirements of each particular field of application, such as scientific discovery, diagnosis, machine 1 I have described my eco-cognitive model of abduction (EC-model) in the recent [21, 23]. 2 I have illustrated the classical and so-called AKM-model of abduction in [19].

View PDFchevron_right
Abduction from logic programs: Semantics and complexity
N. Leone

Theoretical Computer Science, 1997

Abduction{ from observations and a theory, nd using hypotheses an explanation for the observations { gained increasing interest during the last years. This form of reasoning has wide applicability in di erent areas of computer science; in particular, it has been recognized as an important principle of common-sense reasoning.

View PDFchevron_right
Abduction as belief revision
Craig Boutilier

Artificial intelligence, 1995

We propose a model of abduction based on the revision of the epistemic state of an agent. Explanations must be sufficient to induce belief in the sentence to be explained (for instance, some observation), or ensure its consistency with other beliefs, in a manner that adequately accounts for factual and hypothetical sentences. Our model will generate explanations that nonmonotonically predict an observation, thus generalizing most current accounts, which require some deductive relationship between explanation and observation. It also provides a natural preference ordering on explanations, defined in terms of normality or plausibility. To illustrate the generality of our approach, we reconstruct two of the key paradigms for model-based diagnosis, abductive and consistency-based diagnosis, within our framework. This reconstruction provides an alternative semantics for both and extends these systems to accommodate our predictive explanations and semantic preferences on explanations. It also illustrates how more general information can be incorporated in a principled manner.

View PDFchevron_right

References (53)

  1. Atocha Aliseda. Abductive Reasoning. Logical Investigations into Discovery and Explanations. Springer, Synthese Library Vol. 330, 2006.
  2. Atocha Aliseda and Laura Leonides. Hypotheses testing in adaptive logics: an application to medical diagnosis. Logic Journal of the IGPL, 21:915-930, 2013.
  3. Diderik Batens. A survey of inconsistency-adaptive logics. In Diderik Batens, Graham Priest, and Jean-Paul van Bendegem, editors, Frontiers of Paraconsistent Logic, pages 49-73. Baldock: Research Studies Press, Kings College Publication, 2000.
  4. Diderik Batens. A universal logic approach to adaptive logics. Logica Univer- salis, 1:221-242, 2007.
  5. Shai Ben-David and Rachel Ben-Eliyahu-Zohary. A modal logic for subjective default reasoning. Artificial Intelligence, 116:217-236, 2000.
  6. Craig Boutilier and Veronica Becher. Abduction as belief revision. Artificial Intelligence, 77(1):43-94, 1995.
  7. Daniel Campos. On the distinction between Peirce's abduction and Lipton's in- ference to the best explanation. Synthese, 180:419-442, 2011.
  8. Walter Carnielli. Surviving abduction. Logic Journal of IGPL, 14(2):237-256, 2006.
  9. Brian F. Chellas. Basic conditional logic. Journal of Philosophical Logic, 4:133- 153, 1975.
  10. A. Ciampolini and P. Torroni. Using abductive logic agents for modeling the judicial evaluation of criminal evidence. Applied Artificial Intelligence, 18(3- 4):251-275, 2004.
  11. Luca Console and Pietro Torasso. On the co-operation between abductive and temporal reasoning in medical diagnosis. Artificial Intelligence in Medicine, 3(6):291-311, 1991.
  12. Igor Douven. Abduction. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. 2011.
  13. K.T. Fann. Peirce's Theory of Abdcution. The Hague: Martinus Nijhoff, 1970.
  14. Harry G. Frankfurt. Peirce's notion of abduction. The Journal of Philosophy, 55(14):593-597, 1958.
  15. Tjerk Gauderis. Modelling abduction in science by means of a modal adaptive logic. Foundations of Science. In print. DOI:10.1007/s10699-012-9293-8.
  16. G. Harman. The inference to the best explanation. Philosophical Review, 74:88- 95, 1965.
  17. C. Hartshorne and P. Weiss, editors. Collected Papers of Charles Sanders Peirce. Harvard University Press, 1958-1966.
  18. J. Hintikka. What is abduction? the fundamental problem of contemporary epis- temology. Transactions of the Charles S. Peirce Society, 34:503-533, 1998.
  19. Jerry R. Hobbs. Abduction in natural language understanding. In L. Horn and G. Ward, editors, The Handbook of Pragmatics, pages 724-741. Blackwell Pub- lishing Ltd, 2008.
  20. Michael H.G. Hoffmann. 'Theoric transformations' and a new classification of abductive inferences. Transactions of the Charles S. Peirce Society, 46:570-590, 2011.
  21. John Horty. Reasons as Defaults. Oxford University Press, 2012.
  22. John F. Horty. Skepticism and floating conclusions. Artificial Intelligence, 135:55-72, 2002.
  23. A. C. Kakas, R. A. Kowalski, and F. Toni. Abductive logic programming. Journal of Logic and Computation, 2(6):719-770, 1995.
  24. Hans Lycke. A formal explication of the search for explanations: the adaptive logics approach to abductive reasoning. Logic Journal of IGPL, 20(2):497-516, 2012.
  25. Adolfas Mackonis. Inference to the best explanation, coherence and other ex- planatory virtues. Synthese, 190:975-995, 2013.
  26. Lorenzo Magnani. Abduction, Reason, and Science: Processes of Discovery and Explanation. Kluwer-Plenum, New York, 2001.
  27. L. Magnani (ed.). Special issue on formal representations in model-based reason- ing and abduction. Logic Journal of the IGPL, 21(6), 2013.
  28. David Makinson and Karl Schlechta. Floating conclusions and zombie paths: two deep difficulties in the "directly skeptical" approach to defeasible inheritance nets. Artificial Intelligence, 48:199-209, 1991.
  29. Pierre Marquis. Extending abduction from propositional to first-order logic. In Fundamentals of Artificial Intelligence Research (Lecture Notes in Computer Sci- ence Vol. 535), pages 141-155. Springer-Verlag, Berlin, 1991.
  30. Marta Cialdea Mayer and Fiora Pirri. Abduction is not deduction-in-reverse. Logic Journal of the IGPL, 4(1):95-108, 1996.
  31. M.C. Mayer and F. Pirri. First order abduction via tableau and sequent calculi. Bulletin of the IGPL, 1:99-117, 1993.
  32. Joke Meheus. A formal logic for the abduction of singular hypotheses. In D. Dieks, W. Gonzalez, S. Hartmann, T. Uebel, and M. Weber, editors, Expla- nation, Prediction, and Confirmation. New Trends and Old Ones Reconsidered, pages 93-108. Springer, 2011.
  33. Joke Meheus and Diderik Batens. A formal logic for abductive reasoning. Logic Journal of The IGPL, 14:221-236, 2006.
  34. A. Nepomuceno-Fernández, F. Soler-Toscano, and F. Velázquez-Quesada. An epistemic and dynamic approach to abductive reasoning: selecting the best expla- nation. Logic Journal of the IGPL, 21(6):943-961, 2013.
  35. Ilkka Niiniluoto. Hempel's theory of statistical explanation. In J.H. Fetzer, editor, Science, Explanation, and Rationality: The Philosophy of Carl G. Hempel, pages 138-163. Oxford University Press, Oxford, 2000.
  36. H. Prendinger and M. Ishizuka. A creative abduction approach to scientific and knowledge discovery. Knowledge-Based Systems, 18(7):321 -326, 2005.
  37. Graham Priest. An Introduction To Non-Classical Logic (2nd Edition). Cam- bridge University Press, 2008.
  38. Stathis Psillos. Causation and Explanation. Acumen Publishing Limited, Stocks- field, 2002.
  39. Stathis Psillos. Simply the best: a case for abduction. In A.C. Kakas and F. Sadri, editors, Computational Logic: Logic Programming and Beyond, pages 605-625. Springer-Verlag, Berlin, 2002.
  40. Stathis Psillos. Past and contemporary perspectives on explanation. In Theo A.F. Kuipers, editor, General Philosophy of Science. Focal Issues, pages 97-173. North-Holland Publishers, Amsterdam, 2007.
  41. Frederik Van De Putte and Christian Straßer. Three formats of prioritized adaptive logics: a comparative study. Logic Journal of the IGPL, 22:127-159, 2013.
  42. David-Hillel Ruben. Explaining Explanation. Routledge, London/New York, 1990.
  43. Wesley Salmon. Four Decades of Scientific Explanation. University of Minnesota Press, 1990.
  44. G. Schurz. Patterns of abduction. Synthese, 164:201-234, 2008.
  45. Christian Straßer. A deontic logic framework allowing for factual detachment. Journal of Applied Logic, 9(1):61-80, 2011.
  46. Christian Straßer. Adaptively applying modus ponens in conditional logics of normality. Journal of Applied Non-Classical Logic, 22:125-148, 2012.
  47. Christian Straßer. Adaptive Logics for Defeasible Reasoning. Trends in Logic Vol. 38, Springer, 2014.
  48. Paul Thagard. Computational Philosophy of Science. MIT Press, 1988.
  49. David S. Touretzky, John F. Horty, and Richmond H. Thomas. A clash of in- tuitions: The current state of nonmonotonic multiple inheritance systems. In IJCAI-87, pages 476-482. Morgan Kaufmann, 1987.
  50. Bas van Fraassen. The Scientific Image. Oxford: Clarendon Press, 1980.
  51. Peter Verdée. Adaptive logics using the minimal abnormality strategy are π 1 1 - complex. Synthese, 167:93-104, 2009.
  52. Ian Wilson. Explanatory and inferential conditionals. Philosophical Studies, 35:269-278, 1979.
  53. John Woods. Cognitive economics and the logic of abduction. The Review of Symbolic Logic, 5:148-161, 2012.

Related papers

A study on the logic of abduction
F. Pirri

1996

In this paper we present a logic for abduction, namely a language, a semantics and a proof theory where the abductive relation can be expressed. The abductive relation is the relation between a preferred sentence explaining a given observation, in the context of a background theory, and such an observation itself. The proposed logical system, based on a modal approach, captures propositional abduction over a finite language.

View PDFchevron_right
A Formal Logic for Abductive Reasoning
Diderik Batens

Logic Journal of IGPL, 2006

This paper presents and illustrates a formal logic for the abduction of singular hypotheses. The logic has a semantics and a dynamic proof theory that is sound and complete with respect to the semantics. The logic presupposes that, with respect to a specific application, the set of explananda and the set of possible explanantia are disjoint (but not necessarily exhaustive). Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

View PDFchevron_right
On the Relationship Between Abduction and Deduction
Daniele Theseider Dupre

Journal of Logic and Computation, 1991

View PDFchevron_right
Abduction is not Deduction-in-Reverse
F. Pirri

Logic Journal of IGPL, 1996

Abduction is a topic that attracts much interest in AI and automated reasoning research. Di erent approaches have been devised, that give a formalized account of explanatory reasoning, propose methods to compute explanations, frame abduction in the context of logic programming. However, the logical nature of abduction is still far from being clear and di erent speci cations of the key underlying concepts have been given, that make it di cult to speak of abduction as a single wellde ned form of reasoning. This work is a preliminary discussion on the logical nature of abductive reasoning, emphasizing the fundamental di erence between abductive and deductive inference. Some logical properties of the inference to the \best explanation" are put forward and analyzed when the underlying logic is any extension of classical propositional logic (rst order logic, modal logic) or a non monotonic system.

View PDFchevron_right
Abduction, that ubiquitous form of reasoning
Ramón Pinero

Expert Systems with Applications, 1998

In recent years, attention has been devoted to abduction, a hypothetical form of non-monotonic reasoning that tries to fit the best 'explanation' to a given observation. In this paper we present a collection of applications of automated abductive reasoning developed in the Center for Artificial Intelligence of the ITESM (Monterrey, Mexico) in the last five years, covering a range from natural language understanding to software re-use.

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