We propose a logic-based rendition of electronic institutions – these are means to specify open agent organisations. We employ a simple notation based on first-order logic and set theory to represent an expressive class of electronic institutions. We also provide a formal semantics to our constructs and present a distributed implementation of a platform to enact electronic institutions specifie...

Lambda logic is the union of first order logic and lambda calculus. The purpose of this note is to give a complete and precise definition of the syntax of lambda logic, and explain its relations to first order logic and to simple type theory. This is a revised and expanded version of [6].

There are properties of nite structures that are expressible with the use of Hilbert's-operator in a manner that does not depend on the actual interpretation for-terms, but not expressible in plain rst-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in rst-order logic over nite structures. The present result also impl...

By a classifying topos for a first-order theory T, we mean a topos E such that, for any topos F , models of T in F correspond exactly to open geometric morphisms F → E . We show that not every (infinitary) first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate ‘smallness condition’, and we show that every Grothendieck topos arises as the c...

The examination of model-theoretic concepts in the context of general finite-dimensional algebras is a natural problem in applied model theory. Many of the most carefully studied and best understood algebraic objects are finite-dimensional algebras. Furthermore, the finiteness inherent to finite-dimensional algebras suggests that their theories might be amenable to exploration with techniques f...

A notion called Herbrand saturation is shown to provide the modeltheoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.

The general methodology of “algebraizing” logics (cf. [2], [4]) is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved. In this paper we tran...

This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for ,u. The principal results then state: EET(p) plus set induction...