Minimal Polynomial Logic: Properties and Extensions

Equality propositional logic and its extensions

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

THE UNIVERSITY OF BIRMINGHAM Minimal Polynomial Logic: Properties and Extensions

Minimal Polynomial Logic (MPL) is a generalisation of classical propositional logic which allows truth values in the continuous interval 0; 1] and in which propositions are represented by multi-variate polynomials. In previous work 7] we have introduced some properties of MPL and shown that it has two possible semantics: a) it can be considered as a logic for expressing, handling and computing ...

Polynomial Ore Extensions of Baer and p.p.-Rings

On the compactness property of extensions of first-order G"{o}del logic

We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-orde...

Extensions of strongly alpha-reversible rings

We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...