Paola Cattabriga

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This article demonstrates the invalidity of Theorem VI in Gödel’s 1931, showing that propositions (15) and (16), derived from the definition 8.1, in its proof, are false in PA. Introduction. Developed as a consequence of the crisis of the foundation of mathematics due to the discovery of the antinomies, Hilbert’s formalism planned as criterions of adequacy(More)
Türing’s argument that there can be no machine computing the diagonal on the enumeration of the computable sequences is not a demonstration. As well known, Türing historical article of 1936 is the result of a special endeavor focused around the factuality of a general process for algorithmic computation. As resultant formal model his famous abstract(More)
The predicate complementary to the well-known Gödel’s provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness and decidability with regard to Peano Arithmetic and the first order predicate calculus.
This article demonstrates the invalidity of the so-called Gödel’s first incompleteness theorem, showing that propositions (15) and (16), derived from the definition 8.1 in Gödel’s 1931 article, are false. Introduction. Developed as a consequence of the crisis of the foundation of mathematics due to the discovery of the antinomies, Hilbert’s formalism(More)
Introduction. By common consent Russell’s antinomy is the reason for which in Zermelo–Fraenkel set theory, there is no set which comprehends all sets. Furthermore, given any set A, there is no set which contains all sets which are not members of A (in particular, there is no set which is the complement of A) ([7] 40-41). In other words, given any set A, the(More)
Deontic logic (DL) is increasingly recognized as an indispensable tool in such application areas as formal representation of legal knowledge and reasoning, formal specification of computer systems and formal analysis of database integrity constraints. Despite this acknowledgement, there have been few attempts to provide computationally tractable inference(More)
This article demonstrates the invalidity of Theorem VI in Gödel’s monograph of 1931, by showing that (15) xBκ(17Gen r) −→ Bewκ[Sb(r Z(x))], (16) xBκ(17Gen r) −→ Bewκ[Neg(Sb(r Z(x))], (derived by means of definition (8.1) Q(x, y) ≡ xBκ[Sb(y Z(y))] respectively from (3) R(x1, . . . , xn) −→ Bewκ[Sb(r u1...un Z(x1)...Z(xn) )], (4) R(x1, . . . , xn) −→(More)
Usually a default rule A : B/C is intended to mean that if A holds in a state of affairs a B is consistent, then C follows by default. However, C is not a necessary conclusion: different states of affairs are possible (conceivable). According to this view, Meyer and van der Hoek [MvH92] developed a multimodal logic, called S5P(n), for treating non-monotonic(More)