Incompleteness of Behavioral Logics

Incompleteness of Behavioral Logics - 7

Incompleteness results for various behavioral logics are investigated. We show that hidden algebra, observational logic, coherent hidden algebra and other current generalizations of hidden algebra do not admit complete deduction systems for equational behavioral satisfaction. The technique used is reduction from a non-recursively enumerable problem to behavioral validity. In fact we show a stro...

Incompleteness of Behavioral Logics - 24 December 1999

Incompleteness results for behavioral logics are investigated. We show that there is a basic nite behavioral speciication for which the behavioral satisfaction problem is not recursively enumerable, which means that there are no automatic methods for proving all true statements; in particular, behavioral logics do not admit complete deduction systems. This holds for all of the behavioral logics...

Minimal Paradefinite Logics for Reasoning with Incompleteness and Inconsistency

Paradefinite (‘beyond the definite’) logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for defining paradefinite logics, consisting of four-valued matrices, and study the better accepted logics that are induced by these matric...

On the Complexity of the Numerically Definite Syllogistic and Related Fragments

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.

Contents 1 On the Incompleteness of Modal Logics