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.

The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized sim...

We propose a simple but powerful approach to the verification of parameterised systems. The approach is based on modelling the reachability between parameterized states as deducibility between suitable encodings of states by formulae of first-order predicate logic. To establish a safety property, that is non-reachability of unsafe states, the finite model finder is used to find a finite counter...

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...

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...

We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents ⊥. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we...

An abstraction mapping over clausal form theories in first-order predicate calculus is presented that involves the renaming of predicate symbols. This renaming is not 1-1, in the sense that several predicate symbols Ri,.. . , Rn from the original theory are all replaced by a single symbol R in the abstract theory. In order to preserve consistency, however, the clauses that distinguish the Rj's ...