We give a new and improved proof that the shrinkage exponent of De Morgan formulae is 2. Namely, we show that for any Boolean function f : {−1, 1} → {−1, 1}, setting each variable out of x1, . . . , xn with probability 1 − p to a randomly chosen constant, reduces the expected formula size of the function by a factor of O(p). This result is tight and improves the work of H̊astad [H̊as98] by removi...

In my paper [3], recently published in this Journal, I study several aspects of the relations between Belnap's logic B and the class DM of De Morgan lattices. Some of these relations concern a Gentzen system for Belnap's logic, denoted by G B , which was introduced in 1988 by my colleague Ventura Verdú and me (see [5] and [6]); indeed, the study of this Gentzen system within the theory of full ...

Marcos Curty, Marc Jofre, Valerio Pruneri, and Morgan W. Mitchell 1 Escuela de Ingenieŕıa de Telecomunicación, Department of Signal Theory and Communications, University of Vigo, Campus Universitario, 36310 Vigo, Pontevedra, Spain 2 ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain 3 ICREA-Institució Catalana de Recerca i Estudis Avançats...

In this paper we give an axiom system of a non-linear 4-valued logic which we call a de Morgan logic (ML), whose Lindenbaum algebra is the de Morgan algebra with implication (MI-algebra), and show that (1) For every MI-algebra L, there is a quotient MI-algebra L such that it is embeddable to the simplest 4-valued MI-algebra M = {0, a, b, 1}; (2) The Lindenbaum algebra of ML is the MI-algebra; (...

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Mo...

In the application of fuzzy logic to expert systems, fuzzy control, and the like, it is not a single logic that is used, but a plethora of distinct logics. The choice used in a speci…c application is often ad hoc— decided on the basis of empirical factors or mere whim. There is a technical commonality to these logics in that they all arise in the same manner through the speci…cation of an algeb...

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI...

A piggyback duality and a translation process between this one and a Priestley duality for each subvariety of involutive Stone algebras and regular o-De Morgan algebras is presented. As a consequence we describe free algebras and the prime spectrum of each subvariety.