Related papers: Ludique : une logique sans axiome d'identit\'e
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
In our previous work, we proposed the logic obtained from full non-associative Lambek calculus by adding a sort of linear-logical modality. We call this logic non-associative non-commutative intuitionistic linear logic ($\mathbf{NACILL}$,…
Neurosymbolic background knowledge and the expressivity required of its logic can break Machine Learning assumptions about data Independence and Identical Distribution. In this position paper we propose to analyze IID relaxation in a…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
In this article, we have introduced a Logic of Formal Inconsistency (LFI) that we call $\vd$. This logic is non-self-extensional, i.e., the replacement property, or the rule for substitution of equivalents, does not hold. A Hilbert-style…
This paper is an introduction to Lambdix, a lazy Lisp interpreter implemented at the Research Laboratory of Paris XI University (Laboratoire de Recherche en Informatique, Orsay). Lambdix was devised in the course of an investigation into…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes.…
This paper is a theoretical contribution to the debate on the learnability of syntax from a corpus without explicit syntax-specific guidance. Our approach originates in the observable structure of a corpus, which we use to define and…
In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly)…
Epistemic logic is known as a logic that captures the knowledge and beliefs of agents and has undergone various developments since Hintikka (1962). In this paper, we propose a new logic called agent-knowledge logic by taking the product of…
In standard epistemic logic, agent names are usually assumed to be common knowledge implicitly. This is unreasonable for various applications. Inspired by term modal logic and assignment operators in dynamic logic, we introduce a…
In this paper, we address the problem of giving names to predicates in logic rules using Large Language Models (LLMs). In the context of Inductive Logic Programming, various rule generation methods produce rules containing unnamed…
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…
An origin is often an intriguing issue. It becomes doubly intriguing when the logical form of thinking is considered. In this paper we will investigate exactly that: we will conjecture on the origin of basic instruments of logical thinking.…
The logical analysis of data, LAD, is a technique that yields two-class classifiers based on Boolean functions having disjunctive normal form (DNF) representation. Although LAD algorithms employ optimization techniques, the resulting binary…
A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible constants)…
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…
There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…