Kalman, J. A., "A shortest single axiom for the classical equivalential calculus", Notre Dame J. Formal Logic 19(19 141--144.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... PYO P(e(e(e(x,e(y,z) y) e(z,x) PYM In the mid 19 J. Kalman and his studentPeterson undertook a computer assisted investigation of all 630 eleven symbol equivalential theses (distinct up to alphabetical variance) Kalman found another shortest single axiom among these [3], the eleventh. Wenotethat Kalman himself graciously regards this eleventh axiom as simply correcting a misprint in [8] P(e(x,e(e(y,e(z,x) e(z,y) XGK Peterson showed that 612 of the eleven symbol theses were too weak [9 and posed as open questions the status of the remaining seven ....

Kalman, J. A., "A shortest single axiom for the classical equivalential calculus", Notre Dame J. Formal Logic 19(19 141--144.

....design and validation, and, in general, tasks that depend on logical reasoning. Substantial evidence exists that automated reasoning now occupies a significant position in science, for its use has led to answering open questions in finite semigroups [Winker et al. 1981] in logical calculi [Kalman, 1978; Wos et al. 1984; Harris and Fitelson, 2001] in combinatory logic [Wos and McCune, 1988] and in algebra [McCune and Padmanabhan, 1996; McCune et al. 2001] To assess the scope and significance of the various contributions, we discuss in Sections 4 and 5 a number of the questions that have ....

....was used to answer this question, resulting in the discovery of such a semigroup of order 83 [Winker et al. 1981] Later experiments with AURA showed that the smallest semigroup with the desired properties has order 7 and that four such semigroups exist. 2. The Kalman question [Peterson, 1977; Kalman, 1978] concerned the possibility of seven formulas being single axioms for equivalential calculus. With AURA s assistance, each of the four formulas XJL, XKE, XAK, and BXO was shown to be too weak [Wos et al. 1984] and each of the formulas XHK and XHN was shown to be strong enough to serve as a ....

[Article contains additional citation context not shown here]

J. Kalman. A shortest single axiom for the classical equivalential calculus. Notre Dame J. Formal Logic, 19(1):141--4, 1978.

....study asserts that Meredith s axiom is a single axiom for two valued sentential (or propositional) calculus; see [10] I give Meredith s proof in the Appendix. As one sees, the inference rule used in the study is condensed detachment, used by Kalman in his landmark study of equivalential calculus [4, 5]; hyperresolution is used. Typically, in such investigations, the only clauses used to initiate applications of an inference rule are unit clauses. Therefore, for the hot list strategy to be usable, one must include at least one nucleus in the hot list; the cited nucleus is the only such clause in ....

Kalman, J., "A shortest single axiom for the classical equivalential calculus", Notre Dame J. Formal Logic 19, 141--144 (1978).

....steps, I shall, nevertheless, pretend otherwise and cite as my first example John Kalman s research. Kalman is a logician at the University of Auckland in New Zealand. In the late 1970s, he had his own theorem proving program which he heavily used for his research in equivalential calculus [8]. Prompted by his desire to become familiar with our efforts in the field, Kalman visited Argonne and suggested leaving with us seven theorems to attempt to prove with our program. He did not have to wait too long before seeing results. Indeed, ten minutes after he presented the seven theorems, he ....

J. Kalman (1978): A Shortest Single Axiom for the Classical Equivalential Calculus. Notre Dame J. Formal Logic 19(1), 141-144.

....practice in mathematics of omitting many bvious steps (for example, those arising from applying symmetry of equality) In fact, on many an s a occasion, I have heard a logician say that mathematicians only outline proofs. In contrast, in variou reas of logic (such as equivalential calculus [Kalman78,Wos95b] all deduced steps are explicitly s c presented. Further, various areas of logic require the use of a specific inference rule, a rule such a ondensed detachment [Kalman83,Wos95b] Seldom is a specific inference rule cited in a mathematics paper or book. The second property of elegance, ....

Kalman, J., "A shortest single axiom for the classical equivalential calculus", Notre Dame

No context found.

Kalman, J., "A Shortest Single Axiom for the Classical Equivalential Calculusrq, Notre

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC