Quasi-classical logic (QC logic) allows the derivation of non-trivial classical inferences from inconsistent information. A paraconsis-tent, or non-trivializable, logic is, by necessity, a compromise, or weakening , of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in ...

In order to avoid trivial consequences, the derivability relation of relevant logics (RL) does not support the inference rule disjunctive syllogism (DS). In this paper, I will show that the inference rule DS can be added to this derivability relation in a way that doesn’t lead to trivial or irrelevant consequences. To do so, I will rely on the insights gained from the study of inconsistency–ada...

The numerical syllogistic is the extension of the traditional syllogistic with numerical quantifiers of the forms at least C and at most C. It is known that, for the traditional syllogistic, a finite collection of rules, similar in spirit to the classical syllogisms, constitutes a sound and complete proof-system. The question arises as to whether such a proof system exists for the numerical syl...

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...

The publication of the human genome has elicited commentary to the effect that since fewer genes were identified than anticipated, it follows that genes are less important to human biology than anticipated. The flaws in this syllogism are explained in the context of a treatise on how genomes operate and evolve and how genes function to produce embryos and brains. Most of our most cherished huma...

Gödel's theorem does not need an introduction. But it is generally not acknowledged that all instances of Gödel's sentence are vacuous (see below). On the contrary Aristotelian logic permits only sentences that are not vacuous. The consequences of these observations are surprising. What does the article title mean? First of all by " Aristotelian logic " we will understand the logic of the tradi...

This is another contribution to the unending controversy over two Barbaras. My approach problem hopefully quite new: I wish view issue through prism of modal upgrading. Modal upgrading occurs when a subject term that has only been predicated assertorically in premises apodictically either: i) conclusion given syllogism, or; ii) some proposition derived from either syllogism alone or combination...