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 ...

We discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed and essentially unique. Thus, we obtain the surpri...

The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field, and report on our efforts to understand its first-order theory.

We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results relating involutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context. This involves, in particular, a new definition of strong characteristicity. The proof exploits a spectral sequence relating S...