On the undecidability of secondorder unification request pdf. Automated theorem proving in firstorder logic modulo. An automated theoremproving system called tps for proving theorems of first or higherorder logic in automatic, semiautomatic, or interactive mode. Firstorder logic is the most familiar logic to mathematicians. Review alfredo ferro 1993 journal of symbolic logic 58 2. Chapters 49 introduce several techniques in mechanical theorem proving, and chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis. Chapters 2 and 3 constitute an introduction to symbolic logic. Firstorder logic and automated theorem proving i melvin fitting.
This reduction is the first main result of this paper, and it is the starting point for proving some novel results about the undecidability of secondorder unification presented in the rest of the. In the authors words, this book is intended for computer scientists interested in automated theorem proving in classical logic. First order logic is the most familiar logic to mathematicians. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. Firstorder logic and automated theorem proving pdf free. But if a theorem has no proof, then the theorem prover might enter a search without end. Automated theorem proving with extensions of firstorder logic. Automated reasoning over mathematical proof was a major impetus for the development of computer science. Automated theorem proving introduction department of computer. Automated deductioncade17 17th international conference on automated deduction, pittsburgh, pa, usa, june 2000. Firstorder logic and automated theorem proving guide books. This book is intended for computer scientists interested in automated theorem proving in classical logic. Decidability of bounded higherorder unification request pdf. This treatment of methods for automated proving of theorems expressed in logic is carefully and clearly written.
This thesis studies automated theorem proving in firstorder logic and its applications. Originally designed as tools for mathematicians, modern applications of automated theorem provers and proof assistants are much more diverse. Some have philosophers as their intended audience, some mathematicians, some computer scien tists. Firstorder logic and automated theorem proving springerlink. Automated theorem proving in firstorder logic modulo lsv. Logic theorist, an automated reasoner which reproved 38 of the 52. As it follows from the theory of firstorder logic, if a theorem has a proof, the proof will be found by this theorem prover, and shown on the output blue window, on the right.
A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. You may find it useful if you find my course notes too concise. Within computer science formal logic turns up in a number of areas, from pro gram verification to logic programming to artificial intelligence. Logic and proof department of computer science and technology. Computer programs to nd formal proofs of theorems have a history going back nearly half a century. Automated theorem proving atp first emerged in the late 1950s, when. It contains a thorough presentation of formal logic and many proof techniques. Automated theorem proving also known as atp or automated deduction is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Melvin fitting, firstorder logic and automated theorem proving. This book is intended for computer scientists interested in automated theo rem proving in classical logic. Firstorder logic and automated theorem proving philpapers.