Related papers: Non-commutative linear logic fragments with sub-co…
We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
This thesis explores how concepts of formal language theory can be used to study left-orderable groups. It analyses the languages formed by their positive cones and demonstrates how the abstract families of languages (AFLs) in the Chomsky…
We show that products of propositional modal logics containing the logic of reflexive frames T as a factor are embeddable into their single-variable fragments. The proof is a simplified version of the proof, to appear, of a similar result…
Our paper investigates the linear logic of knowledge and time LTK_r with reflexive intransitive time relation. The logic is defined semantically, -- as the set of formulas which are true at special frames with intransitive and reflexive…
This paper presents a novel Chunking-Free In-Context (CFIC) retrieval approach, specifically tailored for Retrieval-Augmented Generation (RAG) systems. Traditional RAG systems often struggle with grounding responses using precise evidence…
We present the logic IBV, which is an intuitionistic version of BV, in the sense that its restriction to the MLL connectives is exactly IMLL, the intuitionistic version of MLL. For this logic we give a deep inference proof system and show…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a…
The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that explains correctly the…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is…
We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…
In-context learning (ICL) can significantly enhance the complex reasoning capabilities of large language models (LLMs), with the key lying in the selection and ordering of demonstration examples. Previous methods typically relied on simple…
Long-context large language models remain computationally expensive to run and often fail to reliably process very long inputs, which makes context compression an important component of many systems. Existing compression approaches…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…