{ "item_title" : "Higher-Order Logic and Type Theory", "item_author" : [" John L. Bell "], "item_description" : "This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined.", "item_img_path" : "https://covers1.booksamillion.com/covers/bam/1/10/898/690/1108986900_b.jpg", "price_data" : { "retail_price" : "25.00", "online_price" : "25.00", "our_price" : "25.00", "club_price" : "25.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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