相关论文: An Effective Fixpoint Semantics for Linear Logic P…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…
Formal, mathematically rigorous programming language semantics are the essential prerequisite for the design of logics and calculi that permit automated reasoning about concurrent programs. We propose a novel modular semantics designed to…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and nonmonotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are…
We study the computational expressivity of proof systems with fixed point operators, within the 'proofs-as-programs' paradigm. We start with a calculus muLJ (due to Clairambault) that extends intuitionistic logic by least and greatest…
Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops…
Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…
In this paper we demonstrate how logic programming systems and Automated first-order logic Theorem Provers (ATPs) can improve the accuracy of Large Language Models (LLMs) for logical reasoning tasks where the baseline performance is given…
Modelling, specifying and reasoning about complex systems requires to process in an integrated fashion declarative and procedural aspects of the target domain. The paper reports on an experiment conducted with a propositional version of…
We introduce a large language model (LLM) based approach to answer complex questions requiring multi-hop numerical reasoning over financial reports. While LLMs have exhibited remarkable performance on various natural language and reasoning…
LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…
Programmers currently enjoy access to a very high number of code repositories and libraries of ever increasing size. The ensuing potential for reuse is however hampered by the fact that searching within all this code becomes an increasingly…
In this paper we present the core of LoCo, a logic-based high-level representation language for expressing configuration problems. LoCo shall allow to model these problems in an intuitive and declarative way, the dynamic aspects of…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…