منابع مشابه
Can Modalities Save Naive Set Theory?
History The late Grisha Mints asked Scott whether a naive set theory could be consistent in modal logic. Here are two modal forms of comprehension: (∃y)(∀x)(x ∈ y ↔ ϕ) (Comp) (∃y)(∀x)(x ∈ y ↔ ϕ) (Comp) At the time (2009) neither he nor Scott knew the answer. In the most commonly used systems, where the Converse Barcan Formula (∀xϕ → ∀xϕ) is derivable, (Comp) follows from another comprehension p...
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In a recent series of papers, I and others have advanced new logical approaches to familiar paradoxes. The key to these approaches is to accept full classical logic, and to accept the principles that cause paradox, while preventing trouble by allowing a certain sort of nontransitivity. Earlier papers have treated paradoxes of truth and vagueness. The present paper will begin to extend the appro...
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The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maxima...
متن کاملModal Reasoning and Rough Set Theory
In this paper, we would like to present some modal logics with semantics based on rough set theory and related notions. In addition to surveying some well-known results about the links between modal logics and rough set theory, we also develop some new applied logics inspired I)y generalized rough set theory. Kcywor(ls: Rough set, modal logic, cpistcmic logic. 1 I n t r o d u c t i o n Tile rou...
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In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in...
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ژورنال
عنوان ژورنال: The Australasian Journal of Logic
سال: 2018
ISSN: 1448-5052
DOI: 10.26686/ajl.v15i2.4859