Intensional first-order logic with types
| Abstract | The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. Some extensions to the type theory are discussed, type polymorphism, and enriching the system with sufficient number theory to account for quantifiers of proportion, such as “most.”. | |||||||||
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Similar books and articlesEdward N. Zalta (1997). The Modal Object Calculus and its Interpretation. In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer.
Reinhard Muskens (2007). Intensional Models for the Theory of Types. Journal of Symbolic Logic 72 (1):98-118.
Paul C. Gilmore (2001). An Intensional Type Theory: Motivation and Cut-Elimination. Journal of Symbolic Logic 66 (1):383-400.
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