## How to Prove Higher Order Theorems in First Order Logic

• In this paper we are interested in using a firstorder theorem prover to prove theorems thatare formulated in some higher order logic. Tothis end we present translations of higher or-der logics into first order logic with flat sortsand equality and give a sufficient criterion forthe soundness of these translations. In addi-tion translations are introduced that are soundand complete with respect to L. Henkin's gen-eral model semantics. Our higher order logicsare based on a restricted type structure in thesense of A. Church, they have typed functionsymbols and predicate symbols, but no sorts.

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Author: Manfred Kerber urn:nbn:de:hbz:386-kluedo-3353 SEKI Report (90,19) Article English 1999 1999 Technische Universität Kaiserslautern 2000/04/03 completeness; higher order logic ; morphism ; second order logic ; soundness ; translation Fachbereich Informatik 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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