Related papers: Relativized hyperequivalence of logic programs for…
Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
In recent research on non-monotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P union R and Q union R have the same answer sets for any other program R. This…
Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially…
Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modeling…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
In the field of Answer Set Programming (ASP), two logic programs are strongly equivalent if they are ordinarily equivalent under any extensions. This property provides a theoretical foundation for studying many aspects of logic programs…
Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice,…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive,…
Analogical reasoning -- the capacity to identify and map structural relationships between different domains -- is fundamental to human cognition and learning. Recent studies have shown that large language models (LLMs) can sometimes match…
In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a…
Parallel programs in high performance computing (HPC) continue to grow in complexity and scale in the exascale era. The diversity in hardware and parallel programming models make developing, optimizing, and maintaining parallel software…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
Large language models (LLMs) are increasingly explored for their reasoning capabilities, yet their ability to perform structured, constraint-based optimization from natural language remains insufficiently understood. This study evaluates…
Strong equivalence between knowledge bases ensures the possibility of replacing one with the other without affecting reasoning outcomes, in any given context. This makes it a crucial property in nonmonotonic formalisms. In particular, the…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
Epistemic Logic Programs (ELPs), that is, Answer Set Programming (ASP) extended with epistemic operators, have received renewed interest in recent years, which led to a flurry of new research, as well as efficient solvers. An important…
Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in Answer-Set Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering…
Comparative reasoning is a process of comparing objects, concepts, or entities to draw conclusions, which constitutes a fundamental cognitive ability. In this paper, we propose a novel framework to pre-train language models for enhancing…