deviding both the subjects and the predicates of the categorical propositions into actuality and verity, afzal al-din khunaji states the actuality-parts as adjectives, but verity-parts in three forms: as simple, as relational and as conditional. since the adjectives are formulated in modern logic by conjunction, we can formulate actuality-parts as conjunctions. verity-parts can be formulated at...

This document contains propositions, proofs, and supplementary discussion supporting claims made in the paper “Symmetric propositions and logical quantifiers,” Journal of philosophical logic, forthcoming (henceforth SPLQ). Unless explicitly mentioned otherwise, all references are internal. Section, but not subsection, headings correspond to those of SPLQ. (The latter has no subsections.)

In this paper we describe a cognitive model based on the systemic approach and on the Autopoiesis theory. The syntactical definition of the model consists of logical propositions but the semantic definition includes, besides the usual truth value assignments, what we call emotional flavors, that correspond to the state of the agent’s body translated into cognitive terms. The combination between...

This paper presents our first efforts toward learning simple logical representations from robot sensory data and thus toward a solution for the perceptual grounding problem [2]. The elements of representations learned by our method are states that correspond to stages during the robot’s experiences, and atomic propositions that describe the states. The states are found by an incremental hidden ...

This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types’. The presentation of linear logic is simplified by basing it on the Logic of Unity. An application to the array update problem is briefly discussed.

It is widely held that propositions perform a plethora of theoretical roles. They are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, the referents of ‘that’-clauses, and the primary bearers of truth. This assumption is often combined with the claim that propositions have their truth-values eternally. Following Kaplan’s ...

Universal algebra [5, 9, 4] is the theory of equalities t = u. It is a simple framework within which we can study mathematical structures, for example groups, rings, and fields. It has also been applied to study the mathematical properties of mathematical truth and computability. For example boolean algebras correspond to classical truth, heyting algebras correspond to intuitionistic truth, cyl...

We present δ-calculus, a computational interpretation of Linear Logic, in the form of a typed process algebra whose structures correspond to Proof Nets, and where typing derivations correspond to linear sequent proofs. Term reduction shares the properties of cut elimination in the logic, and immediately we can obtain a number of inherited qualities, among which are termination, deadlock-freedom...

The original formulation of the Curry–Howard correspondence relates propositional logic to the simply-typed λ-calculus at three levels: the syntax of propositions corresponds to the syntax of types; the proofs of propositions correspond to programs of the corresponding types; and the normalization of proofs corresponds to the evaluation of programs. This rich correspondence has inspired our com...