Algebras and logics of partial quasiary predicates

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.