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 ...

Let K be a set of n non-intersecting objects in 3-space. A depth order of K, if exists, is a linear order < of the objects in K such that if K; L 2 K and K lies vertically below L then K < L. We present a new technique for computing depth orders, and apply it to several special classes of objects. Our results include: (i) If K is a set of n triangles whose xy-projections are alìfat', then a dep...

Generalization operators have long been studied in the area of Conceptual Inductive Learning (Michalski, 1983; De Raedt, 2010). We present an implementation of these learning operators in a prototype system for cooperative query answering. The implementation can however also be used as a usual concept learning mechanism for concepts described in first-order predicate logic. We sketch an extensi...

In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing approach observables form a quotient Dirac bracket algebra. We show that these two algebras are isomorphic. A new realization of the observable algebras through the original Poisson bracket is found.Generators, brackets and pointwise products of ...

We consider the problem of simultaneously compressing a finite set of words by a single grammar. The central result of this paper is the construction of an incompressible sequence of finite word languages. This result is then shown to transfer to tree languages and (via a previously established connection between proof theory and formal language theory) also to formal proofs in first-order pred...

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.