First-Order Logic in the Medvedev Lattice
نویسندگان
چکیده
منابع مشابه
First-Order Logic in the Medvedev Lattice
Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik lattices. However, they only formalised this for propositional logic, while Kolmogorov also discussed the universal quantifier. We extend the work of Medvedev to fi...
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We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-...
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We show that the first order theories of the Medevdev lattice and the Muchnik lattice are both computably isomorphic to the third order theory of true arithmetic.
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We show that the first order theories of the Medevdev lattice and the Muchnik lattice are both computably isomorphic to the third order theory of the natural numbers.
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Uncertainty reasoning is one of the important issues of many research fields, such as artificial intelligence, knowledge-based systems, data-mining etc.. This paper proposes the theory of uncertainty reasoning in the “If...then...” type uncertainty reasoning mode based on the lattice-valued first-order logic Lvfl. The “If...then...” rule presented here is the rule in which both antecedent and c...
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ژورنال
عنوان ژورنال: Studia Logica
سال: 2015
ISSN: 0039-3215,1572-8730
DOI: 10.1007/s11225-015-9615-2