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Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 242 (20 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
A Logic of Argumentation for Reasoning under Uncertainty.
 Computational Intelligence
, 1995
"... We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labelled with a representation of the arguments ..."
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Cited by 145 (8 self)
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We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labelled with a representation of the arguments which support their validity. Arguments may then be aggregated to collect more information about the potential validity of the propositions of interest. We make the notion of aggregation primitive to the logic, and then define strength mappings from sets of arguments to one of a number of possible dictionaries. This provides a uniform framework which incorporates a number of numerical and symbolic techniques for assigning subjective confidences to propositions on the basis of their supporting arguments. These aggregation techniques are also described, with examples. Key words: Uncertain reasoning, epistemic probability, argumentation, nonclassical logics, nonmonotonic reasoning 1. Introd...
Logic Programming and Knowledge Representation  the AProlog perspective
 Artificial Intelligence
, 2002
"... In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs u ..."
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Cited by 98 (1 self)
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In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming build on wellfounded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.
Representing Knowledge in AProlog
"... In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of AProlog, can be used to represent various types of knowledge about the world. By way of example ..."
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Cited by 65 (2 self)
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In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of AProlog, can be used to represent various types of knowledge about the world. By way of example we demonstrate how the corresponding representations together with inference mechanisms associated with AProlog can be used to solve various programming tasks.
A New Logical Characterisation of Stable Models and Answer Sets
 In Proc. of NMELP 96, LNCS 1216
, 1997
"... This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics. We define a nonmonotonic logic, called equilibrium logic, based on the least constructive extension, N2, of the intermediate logic of "hereandthere". We show that on logic programs equilib ..."
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Cited by 59 (15 self)
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This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics. We define a nonmonotonic logic, called equilibrium logic, based on the least constructive extension, N2, of the intermediate logic of "hereandthere". We show that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz. We thereby obtain a very simple characterisation of answer set semantics as a form of minimal model reasoning in N2, while equilibrium logic itself provides a natural generalisation of this semantics to arbitrary theories. We discuss briefly some consequences and applications of this result. 1 Introduction By contrast with the minimal model style of reasoning characteristic of several approaches to the semantics of logic programs, the stable model semantics of Gelfond and Lifschitz [8] was, from the outset, much closer in spirit to the styles of reasoning found in othe...
Reasoning with Prioritized Defaults
 Third International Workshop on Logic Programming and Knowledge Representation, volume 1471 of Lecture Notes in Computer Science
, 1998
"... The purpose of this paper is to investigate the methodology of reasoning with prioritized defaults in the language of logic programs under the answer set semantics. We present a domain independent system of axioms, written as an extended logic program, which defines reasoning with prioritized defaul ..."
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Cited by 53 (5 self)
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The purpose of this paper is to investigate the methodology of reasoning with prioritized defaults in the language of logic programs under the answer set semantics. We present a domain independent system of axioms, written as an extended logic program, which defines reasoning with prioritized defaults. These axioms are used in conjunction with a description of a particular domain encoded in a simple language allowing representation of defaults and their priorities. Such domain descriptions are of course domain dependent and should be specified by the users. We give sufficient conditions for consistency of domain descriptions and illustrate the use of our system by formalizing various examples from the literature. Unlike many other approaches to formalizing reasoning with priorities ours does not require development of the new semantics of the language. Instead, the meaning of statements in the domain description is given by the system of (domain independent) axioms. We believe that in ...
A Survey of Paraconsistent Semantics for Logic Programs
 HANDBOOK OF DEFEASIBLE REASONING AND UNCERTAINTY MANAGEMENT SYSTEMS
, 1998
"... In this chapter we motivate the use of paraconsistency, and survey the most salient paraconsistent semantics for (extended) logic programs, which are briefly defined and explained. Most of the semantics are accompanied with their multivalued model theory, giving them a new perspective. The surv ..."
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Cited by 36 (9 self)
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In this chapter we motivate the use of paraconsistency, and survey the most salient paraconsistent semantics for (extended) logic programs, which are briefly defined and explained. Most of the semantics are accompanied with their multivalued model theory, giving them a new perspective. The survey also presents new results regarding the embedding of part of these semantics into normal logic programs under WellFounded Semantics [20], Partial Stable Model Semantics (or stationary semantics) [48], and Stable Model Semantics [21]. Furthermore, a concise recapitulation of other related paraconsistent formalisms is made. The reader is assumed to have a good knowledge of the semantics of normal logic programs. We believe a comprehensive coverage of the topic as it stands at present is attained here.
Logical Pluralism
 To appear, Special Logic issue of the Australasian Journal of Philosophy
, 2000
"... Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism th ..."
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Cited by 29 (6 self)
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Abstract: A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism there is not one true logic; there are many. There is not always a single answer to the question “is this argument valid?” 1 Logic, Logics and Consequence Anyone acquainted with contemporary Logic knows that there are many socalled logics. 1 But are these logics rightly socalled? Are any of the menagerie of nonclassical logics, such as relevant logics, intuitionistic logic, paraconsistent logics or quantum logics, as deserving of the title ‘logic ’ as classical logic? On the other hand, is classical logic really as deserving of the title ‘logic ’ as relevant logic (or any of the other nonclassical logics)? If so, why so? If not, why not? Logic has a chief subject matter: Logical Consequence. The chief aim of
On the unity of duality
 Special issue on “Classical Logic and Computation
, 2008
"... Most type systems are agnostic regarding the evaluation strategy for the underlying languages, with the value restriction for ML which is absent in Haskell as a notable exception. As type systems become more precise, however, detailed properties of the operational semantics may become visible becaus ..."
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Cited by 21 (2 self)
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Most type systems are agnostic regarding the evaluation strategy for the underlying languages, with the value restriction for ML which is absent in Haskell as a notable exception. As type systems become more precise, however, detailed properties of the operational semantics may become visible because properties captured by the types may be sound under one strategy but not the other. For example, intersection types distinguish between callbyname and callbyvalue functions, because the subtyping law (A → B) ∩ (A → C) ≤ A → (B ∩ C) is unsound for the latter in the presence of effects. In this paper we develop a prooftheoretic framework for analyzing the interaction of types with evaluation order, based on the notion of polarity. Polarity was discovered through linear logic, but we propose a fresh origin in Dummett’s program of justifying the logical laws through alternative verificationist or pragmatist “meaningtheories”, which include a bias towards either introduction or elimination rules. We revisit Dummett’s analysis using the tools of MartinLöf’s judgmental method, and then show how to extend it to a unified polarized logic, with Girard’s “shift ” connectives acting as intermediaries. This logic safely combines intuitionistic and dual intuitionistic reasoning principles, while simultaneously admitting a focusing interpretation for the classical sequent calculus. Then, by applying the CurryHoward isomorphism to polarized logic, we obtain a single programming language in which evaluation order is reflected at the level of types. Different logical notions correspond directly to natural programming constructs, such as patternmatching, explicit substitutions, values and callbyvalue continuations. We give examples demonstrating the expressiveness of the language and type system, and prove a basic but modular type safety result. We conclude with a brief discussion of extensions to the language with additional effects and types, and sketch the sort of explanation this can provide for operationallysensitive typing phenomena. 1