A sound and complete sequent calculus for skeptical consequence in predicate default logic is presented. While skeptical consequence is decidable in the finite propositional case, the move to predicate or infinite the...
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ISBN:
(纸本)3540404945
A sound and complete sequent calculus for skeptical consequence in predicate default logic is presented. While skeptical consequence is decidable in the finite propositional case, the move to predicate or infinite theories increases the complexity of skeptical reasoning to being Π11-complete. This implies the need for sequent rules with countably many premises, and such rules are employed.
We present a new evaluation strategy for functional logic programs described by weakly orthogonal conditional term rewriting systems. Our notion of weakly orthogonal conditional rewrite system extends a notion of Berg...
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ISBN:
(纸本)1581137052
We present a new evaluation strategy for functional logic programs described by weakly orthogonal conditional term rewriting systems. Our notion of weakly orthogonal conditional rewrite system extends a notion of Bergstra and Klop and covers a large part of programs defined by conditional equations. Our strategy combines the flexibility of logic programming (computation of solutions for logic variables) with efficient evaluation methods from functional programming. In particular, it is the first known narrowing strategy for this class of programs that evaluates ground terms deterministically. This is achieved by a transformation of conditional term rewriting systems (CTRS) into unconditional ones which is sound and complete w.r.t. the semantics of the original CTRS. We show that the transformation preserves weak orthogonality for the terms of interest. This property allows us to apply a relatively efficient evaluation strategy for weakly orthogonal unconditional term rewriting systems (parallel narrowing) on the transformed programs.
Ordered Choice logic programming (OCLP) allows for preference-based decision-making with multiple alternatives and without the burden of any form of negation. This complete absence of negation does not weaken the lang...
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Ordered Choice logic programming (OCLP) allows for preference-based decision-making with multiple alternatives and without the burden of any form of negation. This complete absence of negation does not weaken the language as both forms (classical and as-failure) can be intuitively simulated in the language. The semantics of the language is based on the preference between alternatives, yielding both a skeptical and a credulous approach. In this paper we discuss the theoretical basis for the implementation of an OCLP front-end for answer set solvers that can compute both semantics in an efficient manner. Both the basic algorithm and the proposed optimizations can be used in general and are not tailored towards any particular answer set solver.
We use a deep embedding of the display calculus for relation algebras δRA in the logical framework Isabelle/HOL to formalise a new, machine-checked, proof of strong normalisation and cut-elimination for δRA which do...
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We use a deep embedding of the display calculus for relation algebras δRA in the logical framework Isabelle/HOL to formalise a new, machine-checked, proof of strong normalisation and cut-elimination for δRA which does not use measures on the size of derivations. Our formalisation generalises easily to other display calculi and can serve as a basis for formalised proofs of strong normalisation for the classical and intuitionistic versions of a vast range of substructural logics like the Lambek calculus, linear logic, relevant logic, BCK-logic, and their modal extensions. We believe this is the first full formalisation of a strong normalisation result for a sequent system using a logical framework.
We define a notion of fibration on generalized operads (that we call structads) that automatically gives the categorical axiomatization of a large and specific class of multiplicative deductive linear systems, which c...
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We solve the problem of obtaining answers to queries posed to a mediated integration system under the local-as-view paradigm that are consistent wrt to certain global integrity constraints. For this, the query program...
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We solve the problem of obtaining answers to queries posed to a mediated integration system under the local-as-view paradigm that are consistent wrt to certain global integrity constraints. For this, the query program is combined with logic programming specifications under the stable model semantics of the class of minimal global instances, and of the class of their repairs.
This paper defines PT-resolution which is the integration of PT-resolution and approximate reasoning. PT-resolution is a deduction method based on partial intersection and truncation. The integration enables the deduc...
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We propose a logic programming language which makes it possible to define and to reason about rough sets. In particular we show how to test for rough inclusion and rough equality. This extension to our previous work [...
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We integrate an expressive class of description logics (DLs) and answer set programming by extending the latter to support inverted predicates and infinite domains, features that are present in most DLs. The extended ...
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We integrate an expressive class of description logics (DLs) and answer set programming by extending the latter to support inverted predicates and infinite domains, features that are present in most DLs. The extended language, conceptual logic programming (CLP) proves to be a viable alternative for intuitively representing and reasoning nonmonotonically, in a decidable way, with possibly infinite knowledge. Not only can conceptual logic programs (CLPs) simulate finite answer set programming, they are also flexible enough to simulate reasoning in an expressive class of description logics, thus being able to play the role of ontology language, as well as rule language, on the Semantic Web.
We investigate the combination of answer set programming and qualitative optimization techniques. Answer set optimization programs (ASO programs) have two parts. The generating program Pyen produces answer sets repres...
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We investigate the combination of answer set programming and qualitative optimization techniques. Answer set optimization programs (ASO programs) have two parts. The generating program Pyen produces answer sets representing possible solutions. The preference program Ppref expresses user preferences. It induces a preference relation on the answer sets of Pyen based on the degree to which rules are satisfied. We discuss possible applications of ASO programming, give complexity results and propose implementation techniques. We also analyze the relationship between A SO programs and CP-networks.
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