Related papers: Around logical perfection
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…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
It is well-known that natural axiomatic theories are pre-well-ordered by logical strength, according to various characterizations of logical strength such as consistency strength and inclusion of $\Pi^0_1$ theorems. Though these notions of…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
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…
Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a…
This paper studies whether rationality can be computed. Rationality is defined as the use of complete information, which is processed with a perfect biological or physical brain, in an optimized fashion. To compute rationality one needs to…
The literature dealing with G\"{o}del's legacy is largely preoccupied with challenging his philosophical views, regarding them as outdated. We believe that such an approach prevents us from seeing G\"{o}del's views in the right light and…
Mathematical approaches to modeling the mind since the 1950s are reviewed. Difficulties faced by these approaches are related to the fundamental incompleteness of logic discovered by K. G\"odel. A recent mathematical advancement, dynamic…
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…
With the aim of developing the concepts of positive logic and in response to a question that was asked by Poizat in one of his articles, I wrote this article. The main topic is the study of compactness in the extension as a compact…
The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
We analyse so-called computable laws, i.e., laws that can be enforced by automatic procedures. These laws should be logically perfect and unambiguous, but sometimes they are not. We use a regulation on road transport to illustrate this…