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Exp(ASPc): Explaining ASP programs with choice atoms and constraint rules

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arXiv 2021年

作者： Trieu, Ly Ly Son, Tran Cao Balduccini, Marcello New Mexico State University NM United States Saint Joseph's University PA United States

We present an enhancement of exp(ASP), a system that generates explanation graphs for a literal -an atom a or its default negation ∼ a-given an answer set A of a normal logic program P, which explain why is true (or false) given A and P. The new system, exp(ASPc), differs from exp(ASP) in that it supports choice rules and utilizes constraint rules to provide explanation graphs that include information about choices and constraints. © 2021, CC BY.

关键词： logic programming

Unfounded sets for disjunctive hybrid MKNF knowledge bases

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arXiv 2021年

作者： Killen, Spencer You, Jia-Huai University of Alberta Canada

Combining the closed-world reasoning of answer set programming (ASP) with the open-world reasoning of ontologies broadens the space of applications of reasoners. Disjunctive hybrid MKNF knowledge bases succinctly extend ASP and in some cases without increasing the complexity of reasoning tasks. However, in many cases, solver development is lagging behind. As the result, the only known method of solving disjunctive hybrid MKNF knowledge bases is based on guess- and-verify, as formulated by Motik and Rosati in their original work. A main obstacle is understanding how constraint propagation may be performed by a solver, which, in the context of ASP, centers around the computation of unfounded atoms, the atoms that are false given a partial interpretation. In this work, we build towards improving solvers for hybrid MKNF knowledge bases with disjunctive rules: We formalize a notion of unfounded sets for these knowledge bases, identify lower complexity bounds, and demonstrate how we might integrate these developments into a solver. We discuss challenges introduced by ontologies that are not present in the development of solvers for disjunctive logic programs, which warrant some deviations from traditional definitions of unfounded sets. We compare our work with prior definitions of unfounded sets. Copyright © 2021, The Authors. All rights reserved.

关键词： logic programming

Product configuration in answer set programming

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arXiv 2021年

作者： Mishra, Seemran University of Potsdam Germany

This is a preliminary work on configuration knowledge representation which serves as a foundation for building interactive configuration systems in Answer Set programming (ASP). The major concepts of the product configuration problem are identified and discussed with a bike configuration example. A fact format is developed for expressing product knowledge that is domainspecific and can be mapped from other systems. Finally, a domain-independent ASP encoding is provided that represents the concepts in the configuration problem. © 2021, CC BY.

关键词： logic programming

Automata for dynamic answer set solving: Preliminary report

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arXiv 2021年

作者： Cabalar, Pedro Diéguez, Martín Lunas, Susana Hahn Martin Schaub, Torsten University of Corunna Spain Université d’Angers France University of Potsdam Germany

We explore different ways of implementing temporal constraints expressed in an extension of Answer Set programming (ASP) with language constructs from dynamic logic. Foremost, we investigate how automata can be used for enforcing such constraints. The idea is to transform a dynamic constraint into an automaton expressed in terms of a logic program that enforces the satisfaction of the original constraint. What makes this approach attractive is its independence of time stamps and the potential to detect unsatisfiability. On the one hand, we elaborate upon a transformation of dynamic formulas into alternating automata that relies on meta-programming in ASP. This is the first application of reification applied to theory expressions in gringo. On the other hand, we propose two transformations of dynamic formulas into monadic second-order formulas. These can then be used by off-the-shelf tools to construct the corresponding automata. We contrast both approaches empirically with the one of the temporal ASP solver telingo that directly maps dynamic constraints to logic programs. Since this preliminary study is restricted to dynamic formulas in integrity constraints, its implementations and (empirical) results readily apply to conventional linear dynamic logic, too. © 2021, CC0.

关键词： logic programming

Graph-based interpretation of normal logic programs

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arXiv 2021年

作者： Li, Fang Salazar, Elmer Gupta, Gopal The University of Texas at Dallas RichardsonTX75080 United States

In this paper we present a dependency graph-based method for computing the various semantics of normal logic programs. Our method employs conjunction nodes to unambiguously represent the dependency graph of normal logic programs. The dependency graph can be transformed suitably in a semantics preserving manner and re-translated into a equivalent normal logic program. This transformed normal logic program can be augmented with a few rules written in answer set programming (ASP), and the CLINGO system used to compute its answer sets. Depending on how these additional rules are coded in ASP, one can compute models of the original normal logic program under the stable model semantics, the well-founded semantics, or the co-stable model semantics. In each case, justification for each atom in the model is also generated. We report on the implementation of our method as well as its performance evaluation. © 2021, CC BY.

关键词： logic programming

On correctness and completeness of an n queens program

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arXiv 2021年

作者： Drabent, W. Lodzimierz Institute of Computer Science Polish Academy of Sciences ul. Jana Kazimierza 5 Warszawa01-248 Poland Department of Computer and Information Science Linköping University LinköpingS-58183 Sweden

Thom Frühwirth presented a short, elegant and efficient Prolog program for the n queens problem. However the program may be seen as rather tricky and one may not be convinced about its correctness. This paper explains the program in a declarative way, and provides proofs of its correctness and completeness. The specification and the proofs are declarative, i.e. they abstract from any operational semantics. The specification is approximate, it is unnecessary to describe the program's semantics exactly. Despite the program works on non-ground terms, this work employs the standard semantics, based on logical consequence and Herbrand interpretations. Another purpose of the paper is to present an example of precise declarative reasoning about the semantics of a logic *** Codes 68N17 (Primary) 68N30 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： logic programming

A first polynomial non-Clausal Class in Many-Valued logic

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arXiv 2021年

作者： Imaz, Gonzalo E. CSIC Barcelona Spain

The relevance of polynomial formula classes to deductive efficiency motivated their search, and currently, a great number of such classes is known. Nonetheless, they have been exclusively sought in the setting of clausal form and propositional logic, which is of course expressively limiting for real applications. As a consequence, a first polynomial propositional class in non-clausal (NC) form has recently been proposed. Along these lines and towards making NC tractability applicable beyond propositional logic, firstly, we define the Regular many-valued Horn Non-Clausal class, or RH, obtained by suitably amalgamating both regular classes: Horn and NC. Secondly, we demonstrate that the relationship between (1) RH and the regular Horn class is that syntactically RH subsumes the Horn class but that both classes are equivalent semantically;and between (2) RH and the regular non-clausal class is that RH contains all NC formulas whose clausal form is Horn. Thirdly, we define Regular Non-Clausal Unit-Resolution, or RURNC, and prove both that it is complete for RH and that checks its satisfiability in polynomial time. The latter fact shows that our intended goal is reached since RH is many-valued, non-clausal and tractable. As RH and RURNC are, both, basic in the DPLL scheme, the most efficient in propositional logic, and can be extended to some other non-classical logics, we argue that they pave the way for efficient non-clausal DPLL-based approximate reasoning. © 2021, CC BY.

关键词： logic programming

A qualitative theory of cognitive attitudes and their change

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arXiv 2021年

作者： Lorini, Emiliano IRIT-CNRS Toulouse University France

We present a general logical framework for reasoning about agents’ cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire and preference. We also present two extensions of the logic, one by the notion of choice and the other by dynamic operators for belief change and desire change, and we apply the former to the analysis of single-stage games under incomplete information. We provide sound and complete axiomatizations for the basic logic and for its two extensions. The paper is "under consideration in Theory and Practice of logic programming (TPLP)". Copyright © 2021, The Authors. All rights reserved.

关键词： logic programming

Multi-context systems: Dynamics and evolution

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arXiv 2021年

作者： Cabalar, Pedro Costantini, Stefania de Gasperis, Giovanni Formisano, Andrea University of Corunna Spain Università di L’Aquila Italy Università di Perugia GNCS-INdAM Italy

Multi-Context Systems (MCS) model in Computational logic distributed systems composed of heterogeneous sources, or "contexts", interacting via special rules called "bridge rules". In this paper, we consider how to enhance flexibility and generality in bridge-rules definition and application. In particular, we introduce and discuss some formal extensions of MCSs useful for a practical use in dynamic environments, and we try to provide guidelines for implementations. Copyright © 2021, The Authors. All rights reserved.

关键词： logic programming