Abstract:
In the paper we investigate algebras and logics
defined for classes of partial quasiary predicates. Informally speaking,
such predicates are partial predicates defined over partial states
(partial assignments) of variables. Conventional n-ary predicates can
be considered as a special case of quasiary predicates. The notion of
quasiary predicate, as well as the notion of quasiary function, is used
in computer science to represent semantics of computer programs
and their components. We define extended first-order algebras of
partial quasiary predicates and investigate their properties. Based
on such algebras we define a logic with irrefutability consequence
relation. A sequent calculus is constructed for this logic, its soundness
and completeness are proved.
