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In this note, a fully modal proof is given of some conservation results proved in a previous paper by arithmetic means. The proof is based on the extendability of Kripke models. 相似文献
2.
Franco Montagna 《Studia Logica》1980,39(4):347-354
For every sequence |p
n
}
n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula
0
A, called the value ofA inPA with respect to the interpretation.
We show that, ifA is true in every diagonalizable algebra, then, for every,
0
A is a theorem ofPA. 相似文献
3.
The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono's Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order. 相似文献
4.
We investigate many paradigms of identifications for classes of languages (namely: consistent learning, EX learning, learning with finitely many errors, behaviorally correct learning, and behaviorally correct learning with finitely many errors) in a measure-theoretic context, and we relate such paradigms to their analogues in learning on informants. Roughly speaking, the results say that most paradigms in measure-theoretic learning wrt some classes of distributions (called canonical) are equivalent to the corresponding paradigms for identification on informants. 相似文献
5.
The logic of proofs was introduced by Artemov in order to analize the formalization of the concept of proof rather than the concept of provability. In this context, some operations on proofs play a very important role. In this paper, we investigate some very natural operations, paying attention not only to positive information, but also to negative information (i.e. information saying that something cannot be a proof). We give a formalization for a fragment of such a logic of proofs, and we prove that our fragment is complete and decidable. 相似文献
6.
On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic 总被引:1,自引:0,他引:1
The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. 相似文献
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Franco Montagna 《Studia Logica》1980,39(4):355-359
The undecidability of the first-order theory of diagonalizable algebras is shown here. 相似文献
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