Related papers: Ludique : une logique sans axiome d'identit\'e

This thesis is concerned with type-logical grammars and their practical applicability as tools of reasoning about sentence syntax and semantics. The focal point is narrowed to Dutch, a language exhibiting a large degree of word order…

Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of…

Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…

Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical…

The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then…

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…

This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in…

We consider the Lambek calculus, or non-commutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega$-rule, and prove that the derivability problem in this calculus is…

The biduality and reflexivity theorems are known to hold for projective varieties defined over fields of characteristic zero, and to fail in positive characteristic. In this article, we construct a notion of reflexivity and biduality in…

By virtue of linguistic compositionality, few syntactic rules and a finite lexicon can generate an unbounded number of sentences. That is, language, though seemingly high-dimensional, can be explained using relatively few degrees of…

In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…

We examine four approaches for dealing with the logical omniscience problem and their potential applicability: the syntactic approach, awareness, algorithmic knowledge, and impossible possible worlds. Although in some settings these…

This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…

Despite the remarkable capabilities of large language models (LLMs) in natural language understanding and reasoning, they often display undesirable behaviors, such as generating hallucinations and unfaithful reasoning. A prevalent strategy…

We solve the word problem of the identity $x(yz) = (xy)(yz)$ by investigating a certain group describing the geometry of that identity. We also construct a concrete realization of the free system of rank~1 relative to the above identity

Imitation learning is a proven method for creating a policy in the absence of rewards, by leveraging expert demonstrations. In this work, we apply imitation learning to conversation. In doing so, we recover a policy capable of talking to a…

If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument utilizes co-referring names 'a0' and 'a1', and the definition of a functional expression 'The reflection of x = y'. The…

Despite the significant improvements that representation learning via self-supervision has led to when learning from unlabeled data, no methods exist that explain what influences the learned representation. We address this need through our…

Signature-based abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the…

We checked each binary relation on a 5-element set for a given set of properties, including usual ones like asymmetry and less known ones like Euclideanness. Using a poor man's Quine-McCluskey algorithm, we computed prime implicants of…