相关论文: On Modular Termination Proofs of General Logic Pro…
Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness…
This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic…
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (such as functional correctness). Hoare logic has been…
We present a method for verifying partial correctness properties of imperative programs that manipulate integers and arrays by using techniques based on the transformation of constraint logic programs (CLP). We use CLP as a metalanguage for…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…
Program reductions are used widely to simplify reasoning about the correctness of concurrent and distributed programs. In this paper, we propose a general approach to proof simplification of concurrent programs based on exploring generic…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…
Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs.…