Related papers: Beyond the Elementary Representations of Program I…
Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on…
We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…
In this paper we give automata-based representation of LTL-FO$^+$ properties. LTL-FO$^+$ is an extension of LTL that includes first-order quantification over bounded variable, thus greatly increasing the expressivity of the language. An…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work…
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…
Answer set programming (ASP) and planning are two widely used paradigms for solving logic programs with declarative programming. In both cases, the quality of the input programs has a major influence on the quality and performance of the…
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…
Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…
A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
We study abduction in First Order Horn logic theories where all atoms can be abduced and we are looking for preferred solutions with respect to three objective functions: cardinality minimality, coherence, and weighted abduction. We…
Every definite logic program has as its meaning a least Herbrand model with respect to the program-independent ordering "set-inclusion". In the case of normal logic programs there do not exist least models in general. However, according to…
Transformers, as the fundamental deep learning architecture, have demonstrated great capability in reasoning. This paper studies the generalizable first-order logical reasoning ability of transformers with their parameterized knowledge and…
Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…
Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…