Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refuta...

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 ...

This paper is a continuation of the formal theory of intermediate quantifiers (expressions such as most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of ) introduced by Novák in [12]. The theory is a fuzzy-logic formalization of the concept introduced by Peterson in his book [17]. In this paper, we syntactically prove that 105 generalized Aristotle’s syllogism...

objective: the use of hema as a biocompatible material in dentin bonding systems and its potential for clinical applications has been well established. excess water can affect conversion of bonding resins. the aim of this study was to survey the effect of water on the degree of conversion of hema by fourier transform infra-red spectroscopy (ft-ir). materials and methods: in this experimental st...

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...

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...