Related papers: Aristotelian assertoric syllogistic
Robustness of reasoning remains a significant challenge for large language models, and addressing it is essential for the practical applicability of AI-driven reasoning systems. We introduce Semantic Self-Verification (SSV), a novel…
To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.
Mathematicians and philosophers have appealed to categoricity arguments in a surprisingly varied range of contexts. One familiar example calls on second-order categoricity in an attempt to show that the Continuum Hypothesis, despite its…
This is an examination, a commentary, of links between some philosophical views ascribed to G\"odel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure,…
We propose and develop an algebraic approach to revealed preference. Our approach dispenses with non algebraic structure, such as topological assumptions. We provide algebraic axioms of revealed preference that subsume previous, classical…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. After a description of the…
Besides the better-known Nelson's Logic and Paraconsistent Nelson's Logic, in "Negation and separation of concepts in constructive systems" (1959), David Nelson introduced a logic called S with the aim of analyzing the constructive content…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine…
A number of elite thinkers in Europe during the 16th and 17th centuries pursued an agenda which historian Paolo Rossi calls the "quest for a universal language," a quest which was deeply interwoven with the emergence of the scientific…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
Large language models (LLMs) are increasingly evaluated on reasoning tasks, yet their logical abilities remain contested. To address this, we study LLMs' reasoning in a well-defined fragment of logic: syllogistic reasoning. We cast the…
Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context…
An alternative mathematics based on qualitative plurality of finiteness is developed to make non-standard mathematics independent of infinite set theory. The vague concept "accessibility" is used coherently within finite set theory whose…
Abductive Reasoning is a task of inferring the most plausible hypothesis given a set of observations. In literature, the community has approached to solve this challenge by classifying/generating a likely hypothesis that does not contradict…
Besides the better-known Nelson logic (N3) and paraconsistent logic (N4), in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called S. The logic S was originally presented by means of a calculus…