Results 281 to 290 of about 27,177 (320)
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Basic Propositional Calculus I
Mathematical Logic Quarterly, 1998AbstractWe present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the ...
Mohammad Ardeshir, Wim Ruitenburg
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1972
Publisher Summary This chapter presents the application of propositional calculus to propositions each of which has one of two logical values, 0 and 1. The value 0 is assigned to a false proposition and the value 1 is assigned to a true proposition. The disjunction and conjunction of propositions are commutative and associative.
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Publisher Summary This chapter presents the application of propositional calculus to propositions each of which has one of two logical values, 0 and 1. The value 0 is assigned to a false proposition and the value 1 is assigned to a true proposition. The disjunction and conjunction of propositions are commutative and associative.
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On the Complexity of Derivation in Propositional Calculus
1970The question of the minimum complexity of derivation of a given formula in classical propositional calculus is considered in this article and it is proved that estimates of complexity may vary considerably among the various forms of propositional calculus.
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Propositional calculus under adjointness
Fuzzy Sets and Systems, 2002In this paper the author develops a formal system for the class of implications \(A\) and conjunctions \(K\), on partially ordered sets \((L, \leq)\) with top element 1, such that \(A\) and \(K\) are related by adjointness, which means that \(y \leq A(x,z)\) iff \(K(x,y) \leq z\). \(A\) and \(K\) satisfy the neutrality principle (i.e.
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The intuitionistic propositional calculus with quantifiers
Mathematical Notes of the Academy of Sciences of the USSR, 1977Let L be the language of the intuitionistic propositional calculus J completed by the quantifiers ∀ and ∃, and let calculus 2J in language L contain, besides the axioms of J, the axioms ∀xB (x) ⊃ B(y) and B(y) ⊃ ∃xB (x). A Kripke semantics is constructed for 2J and a completeness theorem is proven. A result of D.
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One superintuitionistic calculus of propositions
Algebra and Logic, 1985This paper deals with a propositional superintuitionistic logic L treated in \textit{S. V. Popov}'s paper [Algebra Logika 20, 654-706 (1981; Zbl 0528.03028)]. Though Popov presented L as an example of an undecidable logic, the author proves that a problem mentioned to be undecidable in Popov's proof is decidable.
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A new symbolism for the propositional calculus
Journal of Symbolic Logic, 1954This paper reviews various symbolisms for the two-valued propositional calculus, and introduces a new set of signs which embodies the principles of Leśniewski's symbolism, yet resembles better known signs. This type of symbolism, serving as a diagram, may be used either in place of or as auxiliary to the usual symbolisms.
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THE CLASSICAL PROPOSITIONAL CALCULUS OF ARGUMENTS
Mathematical Logic Quarterly, 1984This paper is an exercise in the proof theory of a propositional logic with 'weak' implication. The arguments are envisaged as three dimensional arrays of signed formulas, with negation handled in terms of sign. There are two kinds of arguments, proofs and refutations. A proof runs down the page from its hypotheses to its conclusions, with conjunctions
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1991
The example at the end of the previous chapter which discovered whether or not a person was on board an aircraft used the logical operators AND and OR. This chapter gives a fuller explanation of these and other logical operators.
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The example at the end of the previous chapter which discovered whether or not a person was on board an aircraft used the logical operators AND and OR. This chapter gives a fuller explanation of these and other logical operators.
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Ideographic computation in the propositional calculus
Journal of Symbolic Logic, 1954This paper will be concerned with an adaptation of Parry's trapezoid symbolism to the solving of problems.In Parry's notation ‘pq’, in particular, sets forth the relationship that obtains when p is true, whether q be true or false. The symbol may also be regarded as manifesting the matrix analysis of p.
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