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(Pure) logic out of probability
dc.contributor.author | Sales Porta, Ton |
dc.date.accessioned | 2007-04-03T08:55:52Z |
dc.date.available | 2007-04-03T08:55:52Z |
dc.date.issued | 1996 |
dc.identifier.issn | 1134-5632 |
dc.identifier.uri | http://hdl.handle.net/2099/2621 |
dc.description.abstract | Today, Logic and Probability are mostly seen as independent fields with a separate history and set of foundations. Against this dominating perception, only a very few people (Laplace, Boole, Peirce) have suspected there was some affinity or relation between them. The truth is they have a considerable common ground which underlies the historical foundation of both disciplines and, in this century, has prompted notable thinkers as Reichenbach [14], Carnap [2] [3] or Popper [12] [13] (and Gaifman [5], Scott & Krauss [21], Fenstad [4], Miller [10] [11], David Lewis [9], Stalnaker [22], Hintikka [7] or Suppes [23]) to consider connection-building treatments of Logic and Probability as desirable. Indeed such a line of thinking can be pursued (this author, for one, attempted it in [15-19]). In so doing, one straightforwardly obtains a logic based on ---as the simple unifying concept--- an additive non-functional truth valuation which, though technically indistinguishable from (axiomatic) Probability, can however be totally ``decontaminated" from parasitical probabilistic interpretations (such as the usual readings of ``event", ``probability" or ``conditioning") and be given instead a strictly logical reading and justification (in terms of ``sentence", ``truth" or ``relativity"). Once some deeply-ingrained reading habits are overcome, the required concepts and formulas flow easily, and the resulting assertion-based sentential calculus becomes a very natural extension of ordinary two-valued reasoning. Furthermore, in the process we get: (a) intuitive geometrical and information-related interpretations of the concepts, (b) a simple theoretical explanation for some poorly justified formulas (intermittently advanced by various authors, some mentioned above),and (c) a semantics ---and a proof theory--- for general assertions that is unproblematically derived and also fully consistent with empirical or ad hoc approximate-reasoning ``Bayesian" formulas found by Artificial Intelligence researchers. |
dc.format.extent | 11 |
dc.language.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica |
dc.relation.ispartof | Mathware & soft computing . 1996 Vol. 3 Núm. 1 [ -2 ]p.137-147 |
dc.rights | Reconeixement-NoComercial-CompartirIgual 3.0 Espanya |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject.other | Sentential logic |
dc.subject.other | Boolean algebra |
dc.subject.other | Logical semantics |
dc.subject.other | Probabilistic semantics |
dc.subject.other | Probability logic |
dc.subject.other | Many-valued logics |
dc.subject.other | Supervaluation |
dc.subject.other | Uncertainty |
dc.subject.other | Rational belief |
dc.subject.other | Proof theory |
dc.title | (Pure) logic out of probability |
dc.type | Article |
dc.subject.lemac | Lògica matemàtica |
dc.subject.lemac | Probabilitats |
dc.subject.ams | Classificació AMS::03 Mathematical logic and foundations::03B General logic |
dc.rights.access | Open Access |
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