Related papers: Joint Tabling of Logic Program Abductions and Upda…
Inductive logic programming is a form of machine learning based on mathematical logic that generates logic programs from given examples and background knowledge. In this project, we extend the Popper ILP system to make use of multi-task…
Adding interaction to logic programming is an essential task. Expressive logics such as linear logic provide a theoretical basis for such a mechanism. Unfortunately, none of the existing linear logic languages can model interactions with…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
This paper explores the integration of hypothetical reasoning into an efficient implementation of the fuzzy logic language Bousi~Prolog. To this end, we first analyse what would be expected from a logic inference system, equipped with what…
Large Language Models (LLMs) trained on petabytes of data are highly compressed repositories of a significant proportion of the knowledge accumulated and distilled so far. In this paper we study techniques to elicit this knowledge in the…
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…
Tabled evaluation is a recognized and powerful technique that overcomes some limitations of traditional Prolog systems in dealing with recursion and redundant sub-computations. We can distinguish two main categories of tabling mechanisms:…
The paper proposes a new static analysis designed to handle open programs, i.e., fragments of programs, with dynamic pointer-linked data structures - in particular, various kinds of lists - that employ advanced low-level pointer operations.…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of \emph{arbitrariness}: the more arbitrary…
Logic programming has long being advocated for legal reasoning, and several approaches have been put forward relying upon explicit representation of the law in logic programming terms. In this position paper we focus on the PROLEG…
In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
Several Prolog implementations include a facility for tabling, an alternative resolution strategy which uses memoisation to avoid redundant duplication of computations. Until relatively recently, tabling has required either low-level…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
We present a scheme for translating logic programs, which may use aggregation and arithmetic, into algebraic expressions that denote bag relations over ground terms of the Herbrand universe. To evaluate queries against these relations, we…
We consider an approach to update nonmonotonic knowledge bases represented as extended logic programs under answer set semantics. New information is incorporated into the current knowledge base subject to a causal rejection principle…
Reasoning about tabular information presents unique challenges to modern NLP approaches which largely rely on pre-trained contextualized embeddings of text. In this paper, we study these challenges through the problem of tabular natural…
This study evaluates the GPT-4 Large Language Model's abductive reasoning in complex fields like medical diagnostics, criminology, and cosmology. Using an interactive interview format, the AI assistant demonstrated reliability in generating…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…