Природа логического знания и вопросы обоснования логических систем.

Abstract

The present approach to the construction of a non-standard semantics is closely connected with the analysis of the nature of logical knowlege. We consider that adequate semantics may be constructed without using the concepts of impossible possible worlds and without the concepts of contradictory or incomplete state descriptions. Instead partially defined predicates are accepted. We consider predicates of truth and falsity to be of this kind - they can be partially defined. We proceed from the idea of the symmetry of concepts of truth and falsity (and this is very important). Falsity is considered as an independent notion not as absence or negation of the truth. Let W be a non-empty set of possible worlds, cp a function, ascribing the pair of sets $$ to propositional variables. $H_1\subseteq W, H_2\subseteq W. \phi_\tau(A)=H_1$ is class of worlds in which A holds (domain of a sentense) $\phi_F(A)=H_2$ - a class of worlds in which $A$ does not hold (anti-domain of a sentence) . The relation between classes $\phi_\tau(A)$ and $\phi_F(A)$ may both satisfy or not satisfy the following conditions:

(1) $\phi_\tau(A)\cap\phi_F(A)=\varnothing$ , (2) $\phi_\tau(A)\cup\phi_F(A)=W$. Accepting both (1) and (2) we get standard semantics. Accepting

(1) and rejecting (2) - semantics with truth value gaps; accepting (2) and rejecting (1) - semantics with glut evaluations; rejecting both (1) and (2) we get relevant semantics. On the basis of concept of domain and anti-domain of proposition from the outset different relations of entailment may be introduced, independently of conditions (1) and (2). It is these notions of entailment, combined with conditions (1) and (2), that determine different logical systems.