Related papers: Correctness and completeness of logic programs

Relative correctness is the property of a program to be more-correct than another with respect to a given specification. Whereas the traditional definition of (absolute) correctness divides candidate program into two classes (correct, and…

Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…

The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…

The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…

Large Language Models (LLMs) trained on petabytes of data are highly compressed repositories of a significant proportion of the knowledge accumulated and distilled so far. In this paper we study techniques to elicit this knowledge in the…

Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…

Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between…

Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible…

Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic…

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…

In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…

Large language models (LLMs) have become essential tools in software development, widely used for requirements engineering, code generation and review tasks. Software engineers often rely on LLMs to assess whether system code implementation…

We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…

Local Completeness Logic (LCL) has been put forward as a program logic for proving both the correctness and incorrectness of program specifications. LCL is an abstract logic, parameterized by an abstract domain that allows combining over-…

Description Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the…

Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…

We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate…