Embedding of Modal Predicate Systems into Lower Predicate Calculus

A Hybrid Predicate Calculus∗

We present the Hybrid Predicate Calculus (HPC), a hybrid logical system which incorporates a fairly conventional first-order predicate calculus, but which also include elements of modal logic and relational algebra. A special effort has been made to produce a (syntactically and semantically) well-integrated whole, rather than just a disjoint union. Our calculus, from a formal point of view, is ...

Dynamic Modal Predicate Logic

The predicate calculus is complete∗

The first thing we need to do is to precisify the inference rules UI and EE. To this end, we will use A(c) to denote a sentence containing the name c, and we will use ∀vA(v) to denote the sentence that results from replacing all occurrences of c in A(c) with v and then putting the quantifier ∀v on the front. (We also require that the variable v did not already occur in A(c).) We use a similar c...

Modal Foundations for Predicate Logic

The complexity of any logical modeling reeects both the intrinsic structure of a topic described and the weight of the formal tools. Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. In this paper, we investigatèlighter' versions of this general purpose tool, by modally`deconstructing' the usual semantics, and locating i...

Induction of Concepts in the Predicate Calculus

P o s i t i v e and n e g a t i v e i ns tances of a concept are assumed to be desc r i bed by a c o n j u n c t i o n o f l i t e r a l s i n the p r e d i c a t e c a l c u l u s , w i t h terms l i m i t e d t o cons tan ts and u n i v e r s a l l y q u a n t i f i e d v a r i a b l e s . A graph r e p r e s e n t a t i o n of a con junc t i o n o f l i t e r a l s , c a l l e d a "p roduc t...