The author has submitted to Mizar Mathematical Library a series of five articles introducing a framework for the formalization of classical first-order model theory. In them, Gödel’s completeness and Lowenheim-Skolem theorems have also been formalized for the countable case, to offer a first application of it and to showcase its utility. This is an overview and commentary on some key aspects of...

We investigate a number of semantic issues which arise, when a language of expressions such as ML, is augmented with constructs for communication and concurrency, as is the case with CML. We construct a simple language of first-order expressions, which includes an operator let.. = . . .in.. .end to provide a form of sequentialisation and a simple form of abstraction, communication constructs, a...

We provide a knowledge compilation technique which deals with the computational intractability of first order reasoning problems. The notion of prime implicates is extended to theory prime implicates in first order case. We provide an algorithm to compute the theory prime implicates of a knowledge base X with respect to a knowledge base Y where both X and Y are assumed to be in Skolem Conjuncti...

When we start doing serious logic, we very quickly find ourselves wanting to talk about sets. ‘Domains of quantification’ are sets, the ‘extensions of predicates’ are subsets of the domain of quantification. And so forth. But note that this does not immediately entangle us with the heavy duty notion of set that it is the business of hard-core mathematical theories like Zermelo-Fraenkel Set Theo...

In this paper we investigate to what extent a very simple and natural ”reachability as deducibility” approach, originating in research on formal methods for security, is applicable to the automated verification of large classes of infinite state and parameterized systems. This approach is based on modeling the reachability between (parameterized) states as deducibility between suitable encoding...

BLOCKIN We BLOCKIN BLOCKIN have BLOCKIN BLOCKIN been asked by the editors of the Journal of Philosophical Logic to write a short comment on his most recent work, published in this issue, based in part on a referee report by one of us, that, unfortunately, did not reach Aldo in time.