Related papers: Ludique : une logique sans axiome d'identit\'e
Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed sometimes, in both everyday discourse and academic research. This indicates that it is necessary to…
Current large language models reason in isolation. Although it is common to sample multiple reasoning paths in parallel, these trajectories do not interact, and often fail in the same redundant ways. We introduce LACE, a framework that…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
We discuss an ongoing line of research in the relational (non topological) semantics of non-distributive logics. The developments we consider are technically rooted in dual characterization results and insights from unified correspondence…
Categorial type logics, pioneered by Lambek, seek a proof-theoretic understanding of natural language syntax by identifying categories with formulas and derivations with proofs. We typically observe an intuitionistic bias: a structural…
We study some aspects of the emergence of logos from chaos on a basal model of the universe using methods and techniques from algorithmic information and Ramsey theories. Thereby an intrinsic and unusual mixture of meaningful and spurious,…
Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
Indexed Linear Logic has been introduced by Ehrhard and Bucciarelli, it can be seen as a logical presentation of non-idempotent intersection types extended through the relational semantics to the full linear logic. We introduce an…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
As an attempt to uncover the topological nature of composition of strategies in game semantics, we present a ``topological'' game for Multiplicative Additive Linear Logic without propositional variables, including cut moves. We recast the…
Symbolic knowledge can provide crucial inductive bias for training neural models, especially in low data regimes. A successful strategy for incorporating such knowledge involves relaxing logical statements into sub-differentiable losses for…
In this paper, we consider an approach introduced in term rewriting for the automatic detection of non-looping non-termination from patterns of rules. We adapt it to logic programming by defining a new unfolding technique that produces…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic knowledge base and actions to change such…
This paper develops a formal logic for guises based on the work of H\'ector-Neri Casta\~neda, who understood relations from an internalist viewpoint, following Leibniz. We introduce a syntax, model theory, and proof theory for an…
To understand texts written in natural language (LN), we use our knowledge about the norms of the domain. Norms allow to infer more implicit information from the text. This kind of information can, in general, be defeasible, but it remains…
We describe a solution of the word problem in free fields (coming from non-commutative polynomials over a commutative field) using elementary linear algebra, provided that the elements are given by minimal linear representations. It relies…
Our manuscript studies linear temporal (with UNTIL and NEXT) logic based at a conception of intransitive time. non-transitive time. In particular, we demonstrate how the notion of knowledge might be represented in such a framework (here we…
Legal judgment prediction (LJP) has become increasingly important in the legal field. In this paper, we identify that existing large language models (LLMs) have significant problems of insufficient reasoning due to a lack of legal…