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The AXIOM System
"... . AXIOM* is a computer algebra system superficially like many others, but fundamentally different in its internal construction, and therefore in the possibilities it offers to its users. In these lecture notes, we will ffl outline the highlevel design of the AXIOM kernel and the AXIOM type system, ..."
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. AXIOM* is a computer algebra system superficially like many others, but fundamentally different in its internal construction, and therefore in the possibilities it offers to its users. In these lecture notes, we will ffl outline the highlevel design of the AXIOM kernel and the AXIOM type system
Soundness and completeness of an axiom system for program verification
 SIAM Journal of Computing
, 1978
"... K. R. Apt pointed out to me that Theorem 3 (completeness) is technically false, because of a problem with initializing newly declared variables. For example, the formula true {begin begin new x; x:= 1 end; begin new x; y: = x end end} y 1 is valid according to the semantics given (because the second ..."
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) in the definition of Comp (A, s, 3, 7r) on p. 74, so that the computation proceeds with a new state s’. Here s ’ is the same as s except for s’(X,/x) 0. To make Y ( complete we would slightly modify Rule 1 (Rule of variable declarations) of the system Y to read x 0 & PY {begin D*; A * end}Oy X
SOUNDNESS AND COMPLETENESS OF AN AXIOM SYSTEM FOR PROGRAM VERIFICATION*
"... Abstract. A simple ALGOLlike language is defined which includes conditional, while, and procedure call statements as well as blocks. A formal interpretive semantics and a Hoare style axiom system are given for the language. The axiom system is proved to be sound, and in a certain sense complete, re ..."
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Abstract. A simple ALGOLlike language is defined which includes conditional, while, and procedure call statements as well as blocks. A formal interpretive semantics and a Hoare style axiom system are given for the language. The axiom system is proved to be sound, and in a certain sense complete
A physical axiom system based on the spirit
"... Abstract This paper established a physical axiom system. By the axiom system we can derive important physical laws such as momentum conservation law, Newton’s second law, Newton’s law of gravity, Schrödinger equation and Maxwell’s equations, simplified existing physical theories and explain some ph ..."
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Abstract This paper established a physical axiom system. By the axiom system we can derive important physical laws such as momentum conservation law, Newton’s second law, Newton’s law of gravity, Schrödinger equation and Maxwell’s equations, simplified existing physical theories and explain some
H.: Towards an axiom system for default logic
 In: Proceedings of the AAAI Conference. (2006
"... Recently, Lakemeyer and Levesque proposed a logic of onlyknowing which precisely captures three forms of nonmonotonic reasoning: Moore’s Autoepistemic Logic, Konolige’s variant based on moderately grounded expansions, and Reiter’s default logic. Defaults have a uniform representation under all three ..."
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fills that gap for the propositional subset: a sound and complete axiom system in the new logic for all three varieties of default reasoning. We also present formal derivations for some examples of default reasoning. Finally we present evidence that it is unlikely that a complete axiom system exists
Kolařík M., Independence of axiom system of basic algebras
 Soft Computing13
"... Abstract We prove that the axiom system of basic algebras as given in Chajda and Emanovský (Discuss Math Gen Algebra Appl 24: [31][32][33][34][35][36][37][38][39][40][41][42] 2004) is not independent. The axiom (BA3) can be deleted and the remaining axioms are shown to be independent. The case when ..."
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Abstract We prove that the axiom system of basic algebras as given in Chajda and Emanovský (Discuss Math Gen Algebra Appl 24: [31][32][33][34][35][36][37][38][39][40][41][42] 2004) is not independent. The axiom (BA3) can be deleted and the remaining axioms are shown to be independent. The case
Axiom Systems for Boolean Algebra Using the Sheffer Stroke
, 2000
"... In this article, we present several new 2axiom systems for Boolean algebra using the Sheer stroke. In each case, we indicate how the given system can be used to derive the system presented by Sheer in 1913 (Sheer[5]). Our search for proofs relied heavily on the use of an automated reasoning program ..."
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In this article, we present several new 2axiom systems for Boolean algebra using the Sheer stroke. In each case, we indicate how the given system can be used to derive the system presented by Sheer in 1913 (Sheer[5]). Our search for proofs relied heavily on the use of an automated reasoning
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