We prove an institutional version of A. Robinson’s Consistency Theorem. This result is then applied to the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for a signature square in order to satisfy the Robinson consistency and Craig interpolation properties.

Henkin, Monk and Tarski gave a compositional semantics for first-order predicate logic. We extend this work by including function symbols in the language and by giving the denotation of the atomic formula as a composition of the denotations of its predicate symbol and of its tuple of arguments. In addition we give the denotation of a term as a composition of the denotations of its function symb...

We investigate algorithms for solving the satisfiability problem in composition-nominative logics of quantifier-equational level. These logics are algebra-based logics of partial predicates constructed in a semantic-syntactic style on the methodological basis, which is common with programming; they can be considered as generalizations of traditional logics on classes of partial predicates that ...

This paper provides formal semantics for an extension of the ObjectRole Modeling approach that supports declaration of dynamic rules. Dynamic rules differ from static rules by pertaining to properties of state transitions, rather than to the states themselves. In this paper we restrict application of dynamic rules to so-called single-step transactions, with an old state (the input of the transa...

Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the λ-binder of the lambda-calculus or the ∀binder of first-order logic. It also allows us to finitely axiomatise arithmetic, and similarly to axiomatise ‘nominal’ datatypes-with-binding. Just like ...

We propose a language which can express every computable query. The language is syntactically based on the first-order predicate calculus, but semantically is interpreted as post-conditions, unlike the customary calculus query languages. The language has a capability to restrict itself to reasonable queries, accepting criteria of reasonability as a parameter.

Let / be any fixed positive integer and a a sentence in the first-order predicate calculus of/unary functions. For positive integers n, an «-structure is a model with universe {0,1,...,« 1} and/unary functions, and p(n,a) is the ratio of the number of «-structures satisfying a to n"f, the number of «-structures. We show that lim„_00/i(«, a) exists for all such a, and its value is given by an ex...

We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased...