Infinite Computation, Co-induction and Computational Logic

Gupta, Gopal; Saeedloei, Neda; DeVries, Brian W.; Min, Richard; Marple, Kyle; Kluźniak, Feliks

doi:10.1007/978-3-642-22944-2_4

Cited by 12 publications

(9 citation statements)

References 23 publications

(36 reference statements)

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“…This semantics is efficiently implemented using the soft-cut control construct found on several Prolog compilers, including all of those that provide the necessary minimal support for rational terms. 4 The following example of the compilation of the coinductive predicate p/1 in Listing 1.1 illustrates our current implementation (with all non-relevant details, including the internal names of the coinductive and preflight predicates, abstracted for clarity of presentation): In the code above, the predicate member/2 has its traditional inductive definition and the (*->)/2 operator denotes the soft-cut control construct, as found on several Prolog compilers such as ECLiPSe, GNU Prolog, SWI-Prolog, and YAP. 5 When the coinductive_success_hook/1 or the coinductive_success_hook/2 hook predicate are defined for a coinductive predicate, they are called in the place of the goal true/0 in the code in Listing 1.4 (the Logtalk compiler looks first for a user definition of the arity two version of the hook predicate).…”

Section: Methodsmentioning

confidence: 99%

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A Portable and Efficient Implementation of Coinductive Logic Programming

Moura

2013

Practical Aspects of Declarative Languages

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Section: Methodsmentioning

confidence: 99%

“…We assume that the reader is familiar with the theoretical work in coinduction (see e.g. [4,5]). Therefore, this paper is written from a practical, technical point-of-view.…”

Section: Introductionmentioning

confidence: 99%

A Portable and Efficient Implementation of Coinductive Logic Programming

Moura

2013

Practical Aspects of Declarative Languages

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“…Coinductive logic programming can be used for reasoning about unfounded sets, behavioral properties of (interactive) pro-grams, etc., as well as elegantly proving liveness properties in model checking, type inference in functional programming, etc. [3].…”

Section: Coinductive Logic Programmingmentioning

confidence: 99%

“…Even with the restriction to rational proofs, there are many applications of coinductive logic programming. These include model checking, modeling ω-automata, non-monotonic reasoning, etc [3].…”

Section: Coinductive Logic Programmingmentioning

confidence: 99%

Coinductive Constraint Logic Programming

Saeedloei

Gupta²

2012

Functional and Logic Programming

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Abstract. Constraint logic programming (CLP) has been proposed as a declarative paradigm for merging constraint solving and logic programming. Recently, coinductive logic programming has been proposed as a powerful extension of logic programming for handling (rational) infinite objects and reasoning about their properties. Coinductive logic programming does not include constraints while CLP's declarative semantics is given in terms of a least fixed-point (i.e., it is inductive) and cannot directly support reasoning about (rational) infinite objects and their properties. In this paper we combine constraint logic programming and coinduction to obtain co-constraint logic programming (co-CLP for brevity). We present the declarative semantics of co-CLP in terms of a greatest fixed-point and its operational semantics based on the coinductive hypothesis rule. We prove the equivalence of these two semantics for programs with rational terms.

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“…Meanwhile, there are also many approaches to solve programs under the well-founded semantics, such as XSB [15] and XOLDTNF [6]. For the co-stable model semantics [16,9], there is no specific solving systems designed yet.…”

Section: Introductionmentioning

confidence: 99%

Graph-based Interpretation of Normal Logic Programs

Li¹,

Salazar²,

Gupta³

2021

Preprint

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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.

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Infinite Computation, Co-induction and Computational Logic

Abstract: Abstract. We give an overview of the coinductive logic programming paradigm. We discuss its applications to modeling ω-automata, model checking, verification, non-monotonic reasoning, developing SAT solvers, etc. We also discuss future research directions.

Cited by 12 publications

References 23 publications

A Portable and Efficient Implementation of Coinductive Logic Programming

A Portable and Efficient Implementation of Coinductive Logic Programming

Coinductive Constraint Logic Programming

Graph-based Interpretation of Normal Logic Programs

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