Kripke models for subtheories of CZF

Kripke models for subtheories of CZF

In this paper a method to construct Kripke models for subtheories of constructive set theory is introduced that uses constructions from classical model theory such as constructible sets and generic extensions. Under the main construction all axioms except the collection axioms can be shown to hold in the constructed Kripke model. It is shown that by carefully choosing the classical models vario...

Refinement of Kripke Models for Dynamics

ions of the Muddy Children for n = 3 children. f (1) = f (2) = A, f (3) = 3 and g = Id . D3 /// means proposition D3 has valuation ? in the current state. Francien Dechesne, Yanjing Wang and Simona Orzan Refinement of Kripke Models for Dynamics Introduction Abstraction/Refinement and Logical Characterization An Example Conclusions Muddy Children Abstraction of n=3 case D1D2D3 /// D1D3 /// 3 A D...

Kripke Models for Classical Logic

We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications.

Submodels of Kripke models

A Kripke model K is a submodel of another Kripke modelM if K is ob tained by restricting the set of nodes ofM In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas This result is an analogue of the Lo s Tarski theorem for the Classical Predicate Calculus In appe...

Kripke-Style models for typed lambda calculus