J. Hsiang. Topics in Automated Theorem Proving and Program Generation. PhD thesis, University of Illinois (USA), 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....answer [Knuth 70] A convergent rewriting system is a complete and terminating decision procedure for determining whether or not an equation is implied by the original set of equations. Term rewriting systems can be used as a basis for automatic theorem provers [Huet 82, Kapur 84, Goguen 80, Hsiang 82] These theorem provers have been used for applications such as checking formal specifications [Goguen 79, Guttag 83, Kownacki 84] interpreting logic programming languages [Dershowitz 83a, Fribourg 84] reasoning about relational databases [Cosmadakis 85] and checking properties of petri nets ....

J. Hsiang, "Topics in Automated Theorem Proving and Program Generation," Ph.D. Thesis, Univ. of Illinois, Urbana-Champaign, November 1982.

....in the system. For our purposes, however, these conditions are not relevant, since we consider already known proofs. For instance, it is known that commutativity is, among others, a problematic equation for rewrite systems, leading to the definition of extensions such as class rewrite systems [15]. Here, if two terms are equal modulo commutativity, this information will have been taken into account in the original proof and the commutativity equation will have been used with one of its possible orientations and it is this orientation that will be considered in the generalized proof. ....

J. Hsiang. Topics in Automated Theorem Proving and Program Generation. PhD thesis, University of Illinois, 1982.

....in the Coq proof development system and this is our main aim for future works. We are also interested in using the reflection mecanism to build efficient decision procedures for tautologies and even to implement decision by refutation for parts of first order logic following works of Hsiang [12]. For tautologies, an implementation of Stalmark s algorithm seems the best choice [10] ....

J. Hsiang, Topics in automated theorem proving and program generation, Thesis, University of Illinois, 1982.

....and show that the last four are complete whereas the first is complete for clausal case. Finally, two open problems related to the Grobner basis method and the odd strategy are discussed. 12.1 Introduction The Boolean ring or first order polynomial based theorem proving began with the work of Hsiang (1982, 1985) Hsiang extended the idea of using Boolean polynomials to represent propositional formulae to the case of first order predicate calculus. Based on the completion procedure of Knuth and Bendix (1970) the N strategy was proposed. Later on, by imitating the framework of Buchberger s ....

Hsiang, J. (1982): Topics in Automated Theorem Proving and Program Generation. Ph.D thesis, UIUCDCS-R-82-1113, Univ. of Illinois at UrbanaChampaign, USA.

....0) 20 sec. Flatten S TESTING 0.8 sec. 2 1 0) 20 sec. Flatten V COLLINS 20.4 sec. 2, nil = 2) 40 sec. 1 3, neg. rat. Stack 1 TESTING 0.1 sec. DJ90, p. 253] 2 1 0) 20 sec. Boolean Ring 1 S TESTING 0.3 sec. HD83] Der87, p. 102] 2 1 0) 20 sec. Boolean Ring 2 S TESTING 0.4 sec. [Hsi82], BL87, p. 152] 2 1 0) 20 sec. Neutral Elements Distributivity S TESTING 0.4 sec. Pau84] Ste91, Example 8.13] 2 1 0) 20 sec. Plus S TESTING 0.6 sec. 2 1 0) 20 sec. Endomorphism Associativity V TESTING 0.1 sec. Bel84] BL87] 2, 2 1 0) 20 sec. map(x) v vx) Endomorphism ....

J. Hsiang. Topics in Automated Theorem Proving and Program Generation, PhD Thesis, University of Illinois, 1982.

....guidance during forward reasoning and to direct the simplification of equations. Besides the use of convergent systems as decision procedures, Lankford [ 1975 ] proposed that completion like methods supplant paramodulation for equational deduction within resolution based theorem provers; later, Hsiang [ 1982 ] showed how a variant of completion can be used in place of resolution for (refutational) theorem proving in first order predicate calculus. Although completion often generates an infinite number of additional rules, and at the same time deletes many old rules, Huet [ 1981 ] demonstrated ....

.... (x; y) and (y; x) and (x; x) x and (x; and (y; z) and (and (x; y) z) xor (x; F ) x xor(x; y) xor(y; x) xor (x; x) F xor (x; xor(y; z) xor(xor (x; y) z) and (xor (x; y) z) xor(and (x; z) and(y; z) This system is convergent, i.e. terminating and Church Rosser modulo AC [ Hsiang, 1982 ] it computes normal forms of Boolean ring expressions that are unique up to permutations under associativity and commutativity. The exclusive or normal form is due to [ Zhegalkin, 1927; Stone, 1936 ] The idea, then, is to put equations that cannot be handled by rewriting into S, placing in ....

J. Hsiang, Topics in automated theorem proving and program generation, Report R-82-1113, Ph.D. thesis, Department of Computer Science, University of Illinois, Urbana, IL (December 1982).

....(5.8) then simplifies rule (5.4) into p 0 (5.9) and rule (5.6) into q 0: 5.10) As the last step of the procedure, rules (5.9) and (5.10) simplifies rule (5.1) into 1 0; 5.11) which means that S is unsatisfiable. Applying Boolean ring formalism to theorem proving was first described in [H82, H85], in which a complete procedure for inputs in clausal form was presented. The main purpose there was aimed at studying complete theorem proving methods for first order logic, and the propositional procedure came as a side result. The first theorem proving method which used both Boolean ring and ....

J. Hsiang, Topics in automated theorem proving and program generation, PhD. Thesis, Univ. of Illinois, Urbana, IL, 1982.

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J. Hsiang. Topics in Automated Theorem Proving and Program Generation. PhD thesis, University of Illinois (USA), 1982.

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J. Hsiang. Topics in Automated Theorem Proving and Program Generation. PhD thesis, University of Illinois, Urbana-Champaign, United States, 1982.

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Jieh Hsiang. Topics in Automated Theorem Proving and Program Generation. PhD Dissertation, University of Illinois at Urbana-Champaign, 1983. Available from University Microfilms International, Ann Arbor, Michigan.

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J. Hsiang. Topics in Automated Theorem Proving and Program Generation. PhD thesis, Department of Computer Science, University of Illinois, Urbana, IL, December 1982. Report R-82-1113.

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