Related papers: Stratified Negation in Limit Datalog Programs
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
This paper proposes an evaluation of the adequacy of the constraint logic programming paradigm for natural language processing. Theoretical aspects of this question have been discussed in several works. We adopt here a pragmatic point of…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the…
Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of…
The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention.…
Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
Computability logic is a formal theory of computational tasks and resources. Formulas in it represent interactive computational problems, and "truth" is understood as algorithmic solvability. Interactive computational problems, in turn, are…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…
Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…
A data language is a set of finite words defined on an infinite alphabet. Data languages are used to express properties associated with data values (domain defined over a countably infinite set). In this paper, we introduce set augmented…
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic…
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 develop an inductive proof-technique to generate imperative programs for pointer data structures from behavioural specifications expressed in the Answer Set Programming (ASP) formalism. ASP is a non-monotonic logic based formalism that…
Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASP^{fs}). We show that…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…