Introduction to higher order categorical logic
Introduction to higher order categorical logic
Truth and modality for knowledge representation
Truth and modality for knowledge representation
Type-theoretical grammar
Conservative Extensions, Interpretations Between Theories and All That!
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Extensional logic of hyperintensions
Conceptual Modelling and Its Theoretical Foundations
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In this paper we present a framework for constructing hyper-intensional semantics for natural language. On this approach, the axiom of extensionality is discarded from the axiom base of a logic. Weaker conditions are specified for the connection between equivalence and identity which prevent the reduction of the former relation to the latter. In addition, by axiomatising an intensional number theory we can provide an internal account of proportional cardinality quantifiers, like most. We use a (pre-)lattice defined in terms of a (pre-)order that models the entailment relation. Possible worlds/situations/indices are then prime filters of propositions in the (pre-)lattice. Truth in a world/situation is then reducible to membership of a prime filter. We showho wthi s approach can be implemented within (i) an intensional higher-order type theory, and (ii) first-order property theory.