This paper represents the third step in the development of EQ-logics. Namely, after developing propositional and higher-order EQ-logics, we focus also on predicate one. First, we give a brief overview of the propositional EQ-logic and then develop syntax and semantics of predicate EQ-logic. Finally, we prove completeness by constructing a model of a consistent theory of EQ-logic from the syntac...

The last chapter presented the general concept of a logic. In this chapter we consider a particular logic | rst order predicate calculus, also known as simply rst order logic. First order logic is by far the most widely studied logic. It was rst formulated by Guttlob Frege in 1879. However, the fundamental semantic properties of rst order logic were not really understood until the work of Skole...

We introduce and study higher-order coalition logic, a multi modal monadic second-order logic with operators [{x}ψ]φ expressing that the coalition of all agents satisfying ψ(x) can achieve a state in which φ holds. We use neighborhood semantics to model extensive games of perfect information with simultaneous actions and we provide a framework reasoning about agents in the same way as it is rea...

This paper shows the use of partial-order assertions and lattice domains for logic programming. We illustrate the paradigm using a variety of examples, ranging from program analysis to deductive databases. These applications are characterized by a need to solve circular constraints and perform aggregate operations. We show in this paper that deening functions with subset assertions and, more ge...

First-order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently several semantics based on counterparts have been examined, in a development that goes back to David Lewis. There is yet another line of research, using intensional objects, that traces back to Richard Montague. I have been invo...

This paper presents the case for the use of higher-order logic as a foundation for computational logic. A suitable polymorphicallytyped, higher-order logic is introduced and its syntax and proof theory briefly described. In addition, a metric space of closed terms suitable for knowledge representation purposes is presented. The approach to representing individuals is illustrated with some examp...

We propose a model theory for full first-order default logic that allows both closed and non-closed default theories. Beginning with first-order languages without logical equality, we note how Henkin’s proof of the completeness theorem for first-order logic yields complete algebras; that is, algebras over which models of consistent theories may always be found. The uniformity is what is interes...

Distributed First Order Logic (DFOL) is a formalism introduced more than 10 years ago with the purpose of formalising distributed knowledge-based systems. In these systems, knowledge is scattered in a set of heterogeneous and interconnected modules. The original version of DFOL defined a set of primitives for the specification of a restricted subset of interconnections between knowledge modules...

Abstract We characterize non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by new notion simulation called meet-simulation. Meet-simulations distinguish themselves from simulations because they relate pairs states one model to single another. En route this result, we use more traditional and prove Hennessy–Milner-style theorem for it, usin...