On the degree of complexity of sentential logics.II. An example of the logic with semi-negation

In this paper being a sequel to our [1] the logic with semi-negation is chosen as an example to elucidate some basic notions of the semantics for sentential calculi. E.g., there are shown some links between the Post number and the degree of complexity of a sentential logic, and it is proved that the degree of complexity of the sentential logic with semi-negation is 20. This is the first known example of a logic with such a degree of complexity. The results of the final part of the paper cast a new light on the scope of the Kripke-style semantics in comparison to the matrix semantics.In memory of Roman Suszko     

Back to the actual future

The purpose of the paper is to rethink the role of actuality in the branching model of possibilities. We investigate the idea that the model should be enriched with an additional factor—the so-called Thin Red Line—which is supposed to represent the single possible course of events that gets actualized in time. We believe that this idea was often misconceived which prompted some unfortunate reactions. On the one hand, it suggested problematic semantic models of future tense and and on the other, it provoked questionable lines of criticism. We reassess the debate and point to potential pitfalls, focusing on the semantic dimension of the Thin Red Line theory. Our agenda transcends the semantics, however. We conclude that semantic considerations do not threaten the Thin Red Line theory and that the proper debate should be carried in the domain of metaphysics.

     

A note on orthogonality of subspaces in Euclidean geometry

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.     

Generalized Pexider equation on a restricted domain

Let X be a normed space and D be a nonempty, open and connected subset of X×X. Inspired by a problem of J. Aczél, we study the functional equation

     

Strong versus weak quantum consequence operations

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic.     

Basic properties of the equivalence

In this paper we investigate some basic semantic and syntactic conditions characterizing the equivalence connective. In particular we define three basic classes of algebras: the class of weak equivalential algebras, the class of equivalential algebras and the class of regular equivalential algebras (see [12]).Weak equivalential algebras can be used to study purely equivalential fragments of relevant logics and strict equivalential fragments of some modal logics (for investigations of strict implicational fragments of modal logics see [20]). Equivalential algebras are suitable to study purely equivalential fragment of BCI and BCK logic (see [21], p. 316). A subclass of the class of regular equivalential algebras is suitable to study equivalential fragments of ukasiewicz logics. Some subvarieties of the class of regular equivalential algebras provide natural semantics for equivalential fragments of the intuitionistic prepositional logic and various intermediate logics (see [13]).The last chapter is a selection of research problems which in the author's opinion are worth to be solved.     

Increasingly cautious sampling,not the black colouration of unpalatable prey,is used by fish in avoidance learning

Animal Cognition - The efficiency of aposematic colouration of prey is based on the innate bias or facilitation of avoidance learning of predators. In many toxic bufonids, larvae are uniformly...