Related papers: Ludique : une logique sans axiome d'identit\'e
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…
A distinguishing property of human intelligence is the ability to flexibly use language in order to communicate complex ideas with other humans in a variety of contexts. Research in natural language dialogue should focus on designing…
We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…
Linear Logic and Defeasible Logic have been adopted to formalise different features relevant to agents: consumption of resources, and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and…
We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well…
In this paper, we discuss different models for human logic systems and describe a game with nature. G\"odel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry…
In this work we propose an alternative formulation to the problem of ground reflectivity grid based localization involving laser scanned data from multiple LIDARs mounted on autonomous vehicles. The driving idea of our localization…
We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two {\it…
In this paper, we give a new linear time correctness condition for proof nets of Multiplicative Linear Logic without units. Our approach is based on a rewriting system over trees. We have only three rewrite rules. Compared with previous…
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
I show that the logic $\textsf{TJK}^{d+}$, one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by (i) dropping the requirement that…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Transformer language models (LMs) have been shown to represent concepts as directions in the latent space of hidden activations. However, for any human-interpretable concept, how can we find its direction in the latent space? We present a…
We conjecture that the relative unpopularity of logical frameworks among practitioners is partly due to their complex meta-languages, which often demand both programming skills and theoretical knowledge of the meta-language in question for…
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…
In order to model in compositional framework some phenomena of lexical pragmatics and in particular the ones studied by Nicholas Asher several contributions developed in our team did use the system F of Jean-Yves Girard to construct logical…
(Maher 2012) introduced an approach for relative expressiveness of defeasible logics, and two notions of relative expressiveness were investigated. Using the first of these definitions of relative expressiveness, we show that all the…