Related papers: Quantitative Constraint Logic Programming for Weig…
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.…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for…
Formal Semantics and Distributional Semantics are two important semantic frameworks in Natural Language Processing (NLP). Cognitive Semantics belongs to the movement of Cognitive Linguistics, which is based on contemporary cognitive…
Partial functions are common abstractions in formal specification notations such as Z, B and Alloy. Conversely, executable programming languages usually provide little or no support for them. In this paper we propose to add partial…
Logic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and, in some cases, more efficient than LP, CLP, or LP with tabling. In this paper we provide insights regarding…
CLP(H) is an instantiation of the general constraint logic programming scheme with the constraint domain of hedges. Hedges are finite sequences of unranked terms, built over variadic function symbols and three kinds of variables: for terms,…
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…
The concurrent logical framework CLF is an extension of the logical framework LF designed to specify concurrent and distributed languages. While it can be used to define a variety of formalisms, reasoning about such languages within CLF has…
Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Results of computational complexity exist for a wide range of phrase structure-based grammar formalisms, while there is an apparent lack of such results for dependency-based formalisms. We here adapt a result on the complexity of…
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…
Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…
One of the long-standing goals in optimisation and constraint programming is to describe a problem in natural language and automatically obtain an executable, efficient model. Large language models appear to bring this vision closer,…
Action description languages, such as A and B, are expressive instruments introduced for formalizing planning domains and planning problem instances. The paper starts by proposing a methodology to encode an action language (with conditional…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…
Controlled natural languages (CNL) with a direct mapping to formal logic have been proposed to improve the usability of knowledge representation systems, query interfaces, and formal specifications. Predictive editors are a popular approach…
We present CLP(BN), a novel approach that aims at expressing Bayesian networks through the constraint logic programming framework. Arguably, an important limitation of traditional Bayesian networks is that they are propositional, and thus…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…