David Pearce

Universidad Politécnica de Madrid, Departamento de Inteligencia Artificial, Faculty Member

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Papers by David Pearce

FQHT: The logic of stable models for logic programs with intensional functions

We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with... more We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of [Bartholomew and Lee, 2012]. We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the approach is demonstrated by showing that it captures the Bartholemew/Lee semantics and satisfies a strong equivalence property.

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Assumption sets for extended logic programs

JFAK. Essays dedicated to Johan van Benthem on the occasion of his 50th birthday, 1999

Generalising the ideas of [10] we define a simple extension of the notion of unfounded set, calle... more Generalising the ideas of [10] we define a simple extension of the notion of unfounded set, called assumption set, that applies to disjunctive logic programs with strong negation. We show that assumption-free interpretations of such extended logic programs coincide with equilibrium models in the sense of [13] and hence with the answer sets of [3, 4].

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Propositional logic based on the dynamics of disbelief

The Logic of Theory Change

Ggrdenfors' (1984) epistemic modelling of intuitionistic propositional logic interprets propositi... more Ggrdenfors' (1984) epistemic modelling of intuitionistic propositional logic interprets propositions as functions from belief states to belief states. In this paper we generMise his approach by including also disbelief, or rejection, as a basic epistemic attitude. Propositions are here defined as ordered pairs of functions on belief states, representing the attitudes of acceptance and rejection, respectively. For this semantics we obtain strong completeness results wrt the constructive logics of Nelson (1949)and Almukdad and Nelson (1984).

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Quantified equilibrium logic and the first order logic of here-and-there

This report continues the study of quantified equilibrium logic, QEL, introduced in [25, 26], and... more This report continues the study of quantified equilibrium logic, QEL, introduced in [25, 26], and its monotonic base logic, here-and-there. We present a slightly modified version of QEL where the so-called unique name assumption or UNA is not assumed from the outset but may be added as a special requirement for specific applications. We also consider here an alternative axiom set for first-order here-and-there. The new system appears to be simpler as well as making it easier to derive some simple semantic ...

On the methodology of possible worlds semantics. I. Correspondence theory

Notre Dame Journal of Formal Logic, 1988

Though possible worlds semantics has long been established as the dominant research tradition in ... more Though possible worlds semantics has long been established as the dominant research tradition in philosophical logic and its applications, its various theories, background assumptions, and norms have seldom been systematically investigated from a methodological point of view. By way of illustration, consider the matter of semantic adequacy. When a new or revised logical system is proposed, the first and often the only significant 'test' to which it is subjected is that of "completeness": Can the logic be shown to be complete with respect to a suitable semantics? Providing the system has a minimum of intrinsic interest, an affirmative answer to this question is virtually a ticket to 'official' recognition, while even incomplete systems of no intrinsic interest whatsoever may acquire, in virtue of their incompleteness, a kind of rarity value in the catalogue of logics. In short, (in)completeness proofs are the mainstay of many a journal article and provide the meat of many logic textbooks. If completeness is genuinely to represent a criterion of internal adequacy, and not merely a logical nicety, we must ask ourselves exactly what cash-value a complete semantics possesses. This question leads naturally to a further problem. Given a well-defined model theory and appropriate rules of interpretation, the matter of completeness is a factual (or better a logical) one, to be settled by formal analysis. But if we are considering logical semantics in general, or one tradition like that of possible worlds in particular, the question is no longer purely logical: it contains a methodological component and can be answered only on the basis of adopting certain conventions. To prove completeness we may need recourse to some nonstandard interpretation of the logical constants, or to some alternative specification of the intended 'models'. Consequently, issues of the following sort arise: Within what limits are we free to modify the stan-*Parts of an earlier version of this paper were presented at the 5th Finnish-Soviet Logic Symposium held in Tampere, Finland, May 1987. For helpful comments on the earlier draft we are grateful to Johan van Benthem and Ingmar Porn.

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Sixty Years of Stable Models

The History and Philosophy of Polish Logic

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The Topology of Common Belief

The Cognitive Foundations of Group Attitudes and Social Interaction, 2015

We study the modal logic K4 C 2 of common belief for normal agents. We study Kripke completeness ... more We study the modal logic K4 C 2 of common belief for normal agents. We study Kripke completeness and show that the logic has tree model property. As a main result we prove that K4 C 2 is the modal logic of all TD-intersection closed, bi-topological spaces with derived set interpretation of modalities. Based on the splitting translation we discuss connections with S4 C 2 , the logic of common knowledge.

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Nonmonotonicity and answer set inference

Logic Programming and Nonmonotonic Reasoning, 1995

The study of abstract properties of nonmonotonic inference has thrown up a number of general cond... more The study of abstract properties of nonmonotonic inference has thrown up a number of general conditions on inference relations that are often thought to be desirable, and sometimes even essential, for an adequate system of nonmonotonic reasoning. However, several of the key conditions on inference that have been proposed in the literature make explicit reference to the classical concept of logical consequence, and there is a general tendency to focus attention on inference operations that are supraclassical in the sense of ...

Stable inference as intuitionistic validity

The Journal of Logic Programming, 1999

The paper characterises the nonmonotonic inference relation associated with the stable model sema... more The paper characterises the nonmonotonic inference relation associated with the stable model semantics for logic programs as follows: a formula is entailed by a program in the stable model semantics if and only if it belongs to every intuitionisticaily complete and consistent extension of the program formed by adding only negated atoms. In place of intuitionistic logic, any proper intermediate logic can be used.

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Disjunctive logic programming, constructivity and strong negation

Lecture Notes in Computer Science

Logic programming research has been based largely on Horn-clause logic, because definite programs... more Logic programming research has been based largely on Horn-clause logic, because definite programs can be interpreted efficiently using SLD-resolution. However, there are several reasons to extend the ideas and concepts of Hornclause logic programming to more general formulas. The paper offers a framework for discussing questions of constructivity and completeness that arise in the field of clause logic programming. Constructive properties of different calculi are investigated and their relation to a certain family of constructive logics ...

An Approach to Minimal Belief via Objective Belief

As a doxastic counterpart to epistemic logic based on S5 we study the modal logic KSD that can be... more As a doxastic counterpart to epistemic logic based on S5 we study the modal logic KSD that can be viewed as an approach to modelling a kind of objective and fair belief. We apply KSD to the problem of minimal belief and develop an alternative approach to nonmonotonic modal logic using a weaker concept of expansion. This corresponds to a certain minimal kind of KSD model and yields a new type of nonmonotonic doxastic reasoning.

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Well-Founded and Partial Stable Semantics Logical Aspects

Lecture Notes in Computer Science, 2009

This paper is devoted to logical aspects of two closely related semantics for logic programs: the... more This paper is devoted to logical aspects of two closely related semantics for logic programs: the partial stable model semantics of Przymusinski [20] and the well-founded semantics of Van Gelder, Ross and Schlipf [24]. For many years the following problem remained open: Which (non-modal) logic can be regarded as yielding an adequate foundation for these semantics in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program? Initial work on this problem was undertaken by ...

Logic programming with strong negation

Lecture Notes in Computer Science

We show how a negation operation which allows for the possibility to represent explicit negative ... more

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A Logical Semantics for Description Logic Programs

Lecture Notes in Computer Science, 2010

We present a new semantics for Description Logic programs (dlprograms) that combine reasoning abo... more We present a new semantics for Description Logic programs (dlprograms) that combine reasoning about ontologies in description logics with non-monotonic rules interpreted under answer set semantics. Our semantics is equivalent to that of , but is more logical in style, being based on the logic QHT of quantified here-and-there that provides a foundation for ordinary logic programs under answer set semantics and removes the need for program reducts. Here we extend the concept of QHT-model to encompass dl-programs. As an application we characterise some logical relations between dl-programs, by mating the idea of QHT-equivalence with the concept of query inseparability taken from description logics.

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Encodings for Equilibrium Logic and Logic Programs with Nested Expressions

Lecture Notes in Computer Science, 2001

Equilibrium logic is an approach to nonmonotonic reasoning that generalises the stable model and ... more Equilibrium logic is an approach to nonmonotonic reasoning that generalises the stable model and answer set semantics for logic programs. We present a method to implement equilibrium logic and, as a special case, stable models for logic programs with nested expressions, based on polynomial reductions to quantified Boolean formulas (QBFs). Since there now exist efficient QBF-solvers, this reduction technique yields a practically relevant approach to rapid prototyping. The reductions for logic programs with nested expressions ...

Minimal Knowledge and Belief via Minimal Topology

Lecture Notes in Computer Science, 2010

We introduce and study a modal logic wK4f that is related to the idea of minimal belief in much t... more We introduce and study a modal logic wK4f that is related to the idea of minimal belief in much the same way as its strengthening, S4F, has been shown to be related to the idea of minimal knowledge. wK4f can be obtained by adding a weakened version of axiom F to the modal logic wK4. We show that, like S4F, wK4f is sound and complete with respect to the class of all minimal topological spaces ie topological spaces with only three open sets. We describe the rooted frames of wK4f by quadruples of natural numbers. Finally we ...

New foundations for metascience

Synthese, 1983

The objective of the present paper is to introduce a new approach to the study of the logical str... more The objective of the present paper is to introduce a new approach to the study of the logical structure of scientific theories. We shall consider, in broad outline, a basic framework for handling theories and for analyzing a number of key metatheoretical concepts. The framework itself may be formally captured within a suitable system of set theory. However, its major innovative and heuristic thrust derives from some notions employed in modern abstract logic; in particular, it encourages the application of model-theoretic concepts and ...

Some Typesmof Equivalence for Logic Programs and Equilibrium Logic

APPIA-GULP-PRODE, 2003

Disjunctive Logic Programming (DLP) under the consistent answer set semantics is an advanced form... more Disjunctive Logic Programming (DLP) under the consistent answer set semantics is an advanced formalism for knowledge representation and reasoning. It is, under widely believed assumptions, strictly more expressive than normal (disjunction-free) logic programming, whose expressiveness is limited to properties decidable in NP. However, this higher expressiveness comes at a computational cost, and while there are now several efficient systems for normal logic programming under the answer set semantics, we are only aware of two serious implementations for the full, disjunctive case. In this paper we investigate a novel technique to couple two main modules usually employed for the implementation of a DLP system more tightly: a model generator (which generates model candidates using a backtracking procedure) and a model checker (which verifies whether such a candidate indeed is an answer set). Instead of using the model checker only as a boolean oracle, in our approach, for every failed check, the model checker also returns a so-called unfounded set. Intuitively, this set provides a diagnosis why the model candidate is not an answer set, and the generator employs this knowledge to backtrack until the set is no longer unfounded, which is vastly more efficient than employing full-fledged model checks to control backtracking. We implemented this approach in DLV, the leading implementation of DLP according to recent comparisons, and experiments on hard benchmark instances indeed show a significant speedup.

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A Characterization of Strong Equivalence for Logic Programs with Variables

Logic Programming and Nonmonotonic Reasoning

On the Logic and Computation of Partial Equilibrium Models

Lecture Notes in Computer Science, 2006

The nonmonotonic formalism of partial equilibrium logic (PEL) was introduced and studied in [1,2]... more The nonmonotonic formalism of partial equilibrium logic (PEL) was introduced and studied in [1,2] and proposed as a logical foundation for the partial stable and well-founded semantics of logic programs. Here we study further logical properties of PEL and some techniques to compute partial equilibrium models.

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