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  • Artikel  (2.427)
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  • 1
    Digitale Medien
    Digitale Medien
    Definite descriptions (1990)
    Springer
    Studia logica 49 (1990), S. 87-104 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract Three views on definite descriptions are summarized and discussed, including that of P. F. Strawson in which reference failure results in lack of truth value. When reference failure is allowed, a problem arises concerning Universal Instantiation. Van Fraassen solves the problem by the use of supervaluations, preserving as well such theorems as ‘a=a’, and ‘Fa ∨ ∼Fa’, even when the term ‘a’ fails to refer. In the present paper a form of relevant, quasi-analytic implication is set out which allows reference failure to infect even ‘a=a’ and ‘Fa ∨ ∼ Fa’ with lack of truth-value. Reference failure causes lack of truth-value in a subwff to spread throughout any wff built up by the classical connectives. As a result none of the classical firstorder axiom schemes remain as axiom schemes in the system presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00401556
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  • 2
    Digitale Medien
    Digitale Medien
    Semantic holism (1990)
    Springer
    Studia logica 49 (1990), S. 67-82 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract A bivalent valuation is snt iff sound (standard PC inference rules take truths only into truths) and non-trivial (not all wffs are assigned the same truth value). Such a valuation is normal iff classically correct for each connective. Carnap knew that there were non-normal snt valuations of PC, and that the gap they revealed between syntax and semantics could be “jumped” as follows. Let VAL snt be the set of snt valuations, and VAL nrm be the set of normal ones. The bottom row in the table for the wedge ‘∨’ is not semantically determined by VAL snt, but if one deletes from VAL snt all those valuations that are not classically correct at the aforementioned row, one jumps straights to VAL nrm and thus to classical semantics. The conjecture we call semantic holism claims that the same thing happens for any semantic indeterminacy in any row in the table of any connective of PC, i.e., to remove it is to jump straight to classical semantics. We show (i) why semantic holism is plausible and (ii) why it is nevertheless false. And (iii) we pose a series of questions concerning the number of possible steps or jumps between the indeterminate semantics given by VAL snt and classical semantics given by VAL nrm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00401554
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  • 3
    Digitale Medien
    Digitale Medien
    On a complexity-based way of constructivizing the recursive functions (1990)
    Springer
    Studia logica 49 (1990), S. 133-149 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract Let g E(m, n)=o mean that n is the Gödel-number of the shortest derivation from E of an equation of the form ϕ(m)=k. Hao Wang suggests that the condition for general recursiveness ∀m∃n(g E(m, n)=o) can be proved constructively if one can find a speedfunction ϕ s s, with ϕ s(m) bounding the number of steps for getting a value of ϕ(m), such that ∀m∃n≦ϕ s(m) s.t. g E(m, n)=o. This idea, he thinks, yields a constructivist notion of an effectively computable function, one that doesn't get us into a vicious circle since we intuitively know, to begin with, that certain proofs are constructive and certain functions effectively computable. This paper gives a broad ‘possibility’ proof for the existence of such classes of effectively computable functions, with Wang's idea of effective computability generalized along a number of dimensions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00401559
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  • 4
    Digitale Medien
    Digitale Medien
    Every world can see a reflexive world (1990)
    Springer
    Studia logica 49 (1990), S. 175-181 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract Let ℭ be the class of frames satisfying the condition $$\forall x\exists y(Ry \wedge yRy)$$ (“every world can see a reflexive world”). LetKMT be the system obtained by adding to the minimal normal modal systemK the axiom $$M((Lp_1 \supset p_1 ) \wedge ... \wedge (Lp_n \supset p_n ))$$ for eachn ⩾ 1. The main results proved are: (1)KMT is characterized by ℭ. (2)KMT has the finite model property. (3) There are frames forKMT which are not in ℭ, but allfinite frames forKMT are in ℭ. (4)KMT is decidable. (5)KMT is not finitely axiomatizable. (6) The class of all frames forKMT is not definable by any formula of first-order logic. (7) 〈W, R〉 is a frame forKMT iff for everyx εW, the worlds thatx can see form a sub-frame which is not finitely colourable.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935597
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  • 5
    Digitale Medien
    Digitale Medien
    Call for papers (1990)
    Springer
    Studia logica 49 (1990), S. 288-288 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935605
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  • 6
    Digitale Medien
    Digitale Medien
    Deontic logic and possible worlds semantics: A historical sketch (1990)
    Springer
    Studia logica 49 (1990), S. 273-282 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract This paper describes and compares the first step in modern semantic theory for deontic logic which appeared in works of Stig Kanger, Jaakko Hintikka, Richard Montague and Saul Kripke in late 50s and early 60s. Moreover, some further developments as well as systematizations are also noted.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935603
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  • 7
    Digitale Medien
    Digitale Medien
    Axiomatization of the De Morgan type rules (1990)
    Springer
    Studia logica 49 (1990), S. 333-343 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract In Section 1 we show that the De Morgan type rules (= sequential rules in L(∨, ⌝) which remain correct if ∧ and ∨ are interchanged) are finitely based. Section 2 contains a similar result for L(→). These results are essentially based on special properties of some equational theories.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00370368
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  • 8
    Digitale Medien
    Digitale Medien
    Temporal necessity and the conditional (1990)
    Springer
    Studia logica 49 (1990), S. 345-363 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract In [12] Richmond Thomason and Anil Gupta investigate a semantics for conditional logic that combines the ideas of [8] and [9] with a branching time model of tense logic. The resulting branching time semantics for the conditional is intended to capture the logical relationship between temporal necessity and the conditional. The central principle of this logical relationship is Past Predominance, according to which past similarities and differences take priority over future similarities and differences in determining the comparative similarity of alternative possible histories with respect to a given present moment. In this paper I will use ordinary possible worlds semantics (i.e. Kripke frames) to solve the completeness problem for a system of logic that combines conditional logic with temporal necessity in the context of Past Predominance. Branching time models turn out not to be necessary for the articulation of Past Predominance, and this means that one can axiomatize Past Predominance without first having to solve a much more difficult problem: the completeness problem for the logic of temporal necessity in the context of branching time. Thomason and Gupta argue in [12] that in addition to Past Predominance, temporal necessity and the conditional are logically related, by what have become known as the Edelberg Inferences, whose apparent validity motivates the very complicated theory presented at the end of [12]. I will conclude this paper by examining how the Edelberg inferences would be incorporated into the possible worlds based system presented in the earlier sections of this paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00370369
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  • 9
    Digitale Medien
    Digitale Medien
    Logical equations and admissible rules of inference with parameters in modal provability logics (1990)
    Springer
    Studia logica 49 (1990), S. 215-239 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman's problem forGL andS. We also show that A. V. Kuznetsov's problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935600
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  • 10
    Digitale Medien
    Digitale Medien
    Klemens Szaniawski (1925–1990) (1990)
    Springer
    Studia logica 49 (1990), S. I 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935594
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