Intuitive semantics for some three-valued logics connected with information, contrariety and subcontrariety
✍ Scribed by Dimiter Vakarelov
- Publisher
- Springer Netherlands
- Year
- 1989
- Tongue
- English
- Weight
- 619 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0039-3215
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✦ Synopsis
Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intm','tive semantics, connected " with the notions of information, contrariety and subcontrariety is given.
1. Four systems of three-valued logic: P3, L3, P3w and L3w
The language of the systems P3 and P3w consits of the following symbols:
VAR an infinite set of propositional variables, ~, 7, 7--three kinds of negations, ^, v -conjunction and disjunction,
9
a special two place connective, (,) -parentheses.
The language of the systems L3 and L3w contains the same symbols but o.
The set FOR of all formulas (in both languages) is defined inductively in the usual way.
Axiom systems. We shall formulate axiom systems for P3 and P3w simultaneously.