Related papers: Strong Equivalence Made Easy: Nested Expressions a…
<Q>_e is the effective list of all finite predicate logic programs. <T_e> is the list of recursive trees. We modify constructions of Marek, Nerode, and Remmel [25] to construct recursive functions f and g such that for all indices e, (i)…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
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…
The Strong equivalence Principle (SEP) states that the description of a physical system in a gravitational field is indistinguishable from the description of the same system at rest in an accelerating frame. While this statement holds true…
Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning…
We present a method for computing stable models of normal logic programs, i.e., logic programs extended with negation, in the presence of predicates with arbitrary terms. Such programs need not have a finite grounding, so traditional…
Learning neural program embeddings is key to utilizing deep neural networks in program languages research --- precise and efficient program representations enable the application of deep models to a wide range of program analysis tasks.…
This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism…
Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka et al. KR 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
Thom Fr\"uhwirth presented a short, elegant and efficient Prolog program for the n queens problem. However the program may be seen as rather tricky and one may be not convinced about its correctness. This paper explains the program in a…
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way is to specify a set of axiomatic equations, and allow proof…
This paper is concerned with the computational complexity of equivalence and minimisation for automata with transition weights in the field Q of rational numbers. We use polynomial identity testing and the Isolation Lemma to obtain…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
An approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of…
In this paper, we study the weighted difference substitutions from geometrical views. First, we give the geometric meanings of the weighted difference substitutions, and introduce the concept of convergence of the sequence of substitution…