Can I read Propositional Calculus Under Adjointness on EtoBox?

Propositional Calculus Under Adjointness by Nehad N. Morsi is a Computer Science article available to read on EtoBox.

What is Propositional Calculus Under Adjointness about?

We develop a formal system for the class of all implications A and conjunctions K, on partially ordered sets (L; 6) with top elements 1, such that A and K are related by adjointness and they satisfy the neutrality principle (that is, 1 is their left identity element). We call the resulting logic propositional calculus under adjointness, abbreviated AdjPC. Most algebraic theorems on those (L; 6); A and K are inequalities in the posets (L; 6) of truth values. In consequence, we have to ÿnd means for abstracting inequalities within syntax; which must be free from partial truth values. This is achieved by employing a further, implication-like adjoint H of A and K, whereby the partial order of (L; 6) coincides with the binary relation H (•; •) = 1. Accordingly, the semantical domain for AdjPC should become the class of all such quintuples (L; 6 ; A; K; H ), which we call adjointness algebras. Our axiom scheme for AdjPC features seven axioms. However, it may be the case that no ÿnite set of axioms can complete AdjPC if inference is carried out by means of modus ponens (MP) alone. This is because AdjPC is too general; it lacks some basic theorems of the more restricted logics (such as res

Who reads Propositional Calculus Under Adjointness?

Author

Nehad N. Morsi

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0165-0114)

Published

2002

Language

EN

Field

Computer Science (Physical Sciences)