David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 94 (3):307 - 330 (2010)
The paper presents an infinite hierarchy PR m [ m = 1, 2, . . . ] of sound and complete axiomatic systems for modal logic with graded probabilistic modalities , which are to reflect what I have elsewhere called the Bolding-Ekelöf degrees of evidential strength as applied to the establishment of matters of fact in law-courts. Our present approach is seen to differ from earlier work by the author in that it treats the logic of these graded modalities not only from a semantical or model-theoretic viewpoint but from a prooftheoretical and axiomatic stance as well. A paramount feature of the approach is its use of so-called systematic frame constants as labels of diverse grades of probability. Apart from this novel feature our approach can be seen to go back to pioneering work by Lou Goble in 1970.
|Keywords||Philosophy Computational Linguistics Mathematical Logic and Foundations Logic|
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References found in this work BETA
L. Jonathan Cohen (1977). The Probable and the Provable. Clarendon Press.
Gilbert H. Harman (1965). The Inference to the Best Explanation. Philosophical Review 74 (1):88-95.
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Saul A. Kripke (1963). Semantical Analysis of Modal Logic I. Normal Propositional Calculi. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
Michael S. Pardo & Ronald J. Allen (2008). Juridical Proof and the Best Explanation. Law and Philosophy 27 (3):223 - 268.
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