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D. C. McCarty 《Journal of Philosophical Logic》1996,25(5):559-565
Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article. 相似文献
24.
Alessandro Avellone Camillo Fiorentini Paolo Mantovani Pierangelo Miglioli 《Studia Logica》1996,57(2-3):373-408
We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.Presented by H. Ono 相似文献
25.
We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or pre-supposes, a certain context in which a primary obligation is already violated. This framework is presented initially as an extension of Standard Deontic Logic (SDL), a normal modal logic of type KD, and is illustrated by application to a series of examples. The concluding section is concerned with some resemblances between CTD and defeasible reasoning. We show first that the SDL-based framework contains a flaw and must be adjusted. A discussion of possible adjustments, including an alternative treatment in terms of a preference-based semantics, reveals difficulties that are reminiscent of problems in defeasible reasoning and intensional accounts of defeasible conditionals. 相似文献
26.
Quantum MV algebras 总被引:1,自引:0,他引:1
Roberto Giuntini 《Studia Logica》1996,56(3):393-417
We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.I should like to thank Prof. M.L. Dalla Chiara and Dr. P. Minari for many interesting comments and remarks.
Daniele Mundici 相似文献
27.
Alasdair Urquhart 《Studia Logica》1996,56(1-2):263-276
This paper defines a category of bounded distributive lattice-ordered grupoids with a left-residual operation that corresponds to a weak system in the family of relevant logics. Algebras corresponding to stronger systems are obtained by adding further postulates. A duality theoey piggy-backed on the Priestley duality theory for distributive lattices is developed for these algebras. The duality theory is then applied in providing characterizations of the dual spaces corresponding to stronger relevant logics.The author gratefully acknowledges the support of the National Sciences and Engineering Research Council of Canada. 相似文献
28.
This paper presents a nonmonotonic deontic logic based on commonsense entailment. It establishes criteria a successful account of obligation should satisfy, and develops a theory that satisfies them. The theory includes two conditional notions of prima facie obligation. One is constitutive; the other is epistemic, and follows nonmonotonically from the constitutive notion. The paper defines unconditional notions of prima facie obligation in terms of the conditional notions. 相似文献
29.
Carlos E. Alchourrón 《Studia Logica》1996,57(1):5-18
The purpose of the paper is to present a logical framework that allow to formalize a kind of prima facie duties, defeasible conditional duties, indefeasible conditional duties and actual (indefeasible) duties, as well as to show their logical interconnections. 相似文献
30.
The current paradigm in medicine generally distinguishes between genetic and environmental causes of disease. Although the word paradigm has become a commonplace, the theories of Thomas Kuhn have not received much attention in the journals of medicine. Kuhn's structuralist method differs radically from the daily activities of the scientific method itself. Using linguistic theory, this essay offers a structuralist reading of Thomas Kuhn's The Structure of Scientific Revolutions. Our purpose is to highlight the similarities between these structuralist models of science and language. In part, we focus on the logic that enables Kuhn to assert the priority of perception over interpretation in the history of science. To illustrate some of these issues, we refer to the distinction between environmental and genetic causes of disease. While the activity of scientific research results in the revision of concepts in science, the production of significant differences that shape our knowledge is in part a social and linguistic process. 相似文献