The paper has a form of a survey on basics of logical geometry and consists of three parts. It is focused on the relationship between many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on important model-theoretic concepts. Our aim is to show that both approaches go in parallel and there are bridges which allow to transfer results, notions and problems bac...

We here present a sufficient condition for general arrowing problems to be non definable in first order logic, based in well known tools of finite model theory e.g. Hanf’s Theorem and known concepts in finite combinatorics, like senders and determiners.

In this paper we report on the formalization of the Tietze extension theorem using the MIZAR system. This theorem has been formalized as a part of the project aimed at formalizing the Jordan curve theorem. However, this development has turned out to be also useful for other formalizations.

Two questions concerning Anselm of Canterbury’s theistic argument provided in Proslogion Ch. 2 are asked and answered: is the argument valid? under what conditions could it be sound? In order to answer the questions the argument is formalized as a first-order theory called AP2. The argument turns out to be valid, although it contains a hidden premise. The argument is also claimed not to be onto...

We prove an Omitting Types Theorem for the extension of first order logic studied by Németi, Sain and others as a solution to the so-called Finitization Problem in Algebraic Logic. A new omitting types theorem for first order logic is obtained.

We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]...

Let C be a class of ordered algebras of a given fixed type τ . Associated with the type is a first order language Lτ , which must also contain a binary predicate to be interpreted by the ordering in members of C. One can then ask the question, when is the class C axiomatisable by sentences of Lτ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a ...

This paper presents an extension of the inverse resolution framework, which is a logical model of theory induction in first order logic. We first propose a definition of completeness for inductive procedures and exhibit some limitations of inverse resolution with respect to this definition. We then propose our model of inversion of logical entailment that extends inverse resolution with regard ...

We present two different formalizations of Equational Predicate Logic, that is, first order logic that uses Leibniz’s substitution of “equals for equals” as a primary rule of inference. We prove that both versions are sound and complete. A by-product of this study is an alternative proof to that contained in [GS3], that the “full” Leibniz rule is strictly stronger than the “no-capture” Leibniz ...