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Logic and probabilistic systems
Archive for Mathematical Logic, 1996The notion of a probabilistic system, based on the two predicates of the form \(R (\varphi, q) =\) ``the probability value of \(\varphi\) is eventually \(\leq q\)'' and \(S (\varphi, q) = \) ``the probability value of \(\varphi\) is eventually \(\geq q\)'', can be defined as a pair \(\langle R,S \rangle\) of relations between sentences and rational ...
MONTAGNA F., SIMI G., SORBI A.
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Artificial Intelligence, 1986
Als Verallgemeinerung der klassischen Logik wird eine Logik mit Wahrheitswerten zwischen 0 und 1 vorgestellt. Techniken zur Berechnung der Wahrscheinlichkeit von Folgerungen und bedingten Wahrscheinlichkeiten, u.a. eine approximative Methode, werden angegeben.
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Als Verallgemeinerung der klassischen Logik wird eine Logik mit Wahrheitswerten zwischen 0 und 1 vorgestellt. Techniken zur Berechnung der Wahrscheinlichkeit von Folgerungen und bedingten Wahrscheinlichkeiten, u.a. eine approximative Methode, werden angegeben.
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1990
Because many artificial intelligence applications require the ability to reason with uncertain knowledge, it is important to seek appropriate generalizations of logic for that case. Nils J. Nilsson [1] presented a semantical generalization of logic in which the truth values of sentences are probability values between 0 and 1.
Victor Lesser, J. W. Guan
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Because many artificial intelligence applications require the ability to reason with uncertain knowledge, it is important to seek appropriate generalizations of logic for that case. Nils J. Nilsson [1] presented a semantical generalization of logic in which the truth values of sentences are probability values between 0 and 1.
Victor Lesser, J. W. Guan
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Probabilistic forcing in quantum logics [PDF]
International Journal of Theoretical Physics, 1993 It is shown that orthomodular lattice can be axiomatized as an ortholattice with a unique operation of identity (bi-implication) instead of the operation of implication and a corresponding algebraic unified quantum logic is formulated. A statistical YES-NO physical interpretation of the quantum logical propositions is then provided to establish a ...
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2020
This chapter presents the proof-theoretical and model-theoretical approaches to reasoning about time and probability. Three different ways of combining probabilistic and temporal modalities are presented, and well defined syntax and corresponding semantics is provided for every formalism.
Aleksandar Perović, Dragan Doder
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This chapter presents the proof-theoretical and model-theoretical approaches to reasoning about time and probability. Three different ways of combining probabilistic and temporal modalities are presented, and well defined syntax and corresponding semantics is provided for every formalism.
Aleksandar Perović, Dragan Doder
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2013
In a seminal paper Goldfarb (1979) points out that ”The connection between quantifiers and choice functions or, more precisely, between quantifier-dependence and choice functions, is at the heart of how classical logicians in the twenties viewed the nature of quantification.” (Goldfarb 1979, p. 357).
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In a seminal paper Goldfarb (1979) points out that ”The connection between quantifiers and choice functions or, more precisely, between quantifier-dependence and choice functions, is at the heart of how classical logicians in the twenties viewed the nature of quantification.” (Goldfarb 1979, p. 357).
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Probabilistic Logic and Induction
Journal of Logic and Computation, 2005Summary: We give a probabilistic interpretation of first-order formulas based on Valiant's model of pac-learning. We study the resulting notion of probabilistic or approximate truth and take some first steps in developing its model theory. In particular we show that every fixed error parameter determining the precision of universal quantification gives
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Probabilistic Entailment and a Non-Probabilistic Logic
Logic Journal of IGPL, 2003Let \(L\) be a finite language of propositional logic. We say that \(\Gamma\), a set of \(m\) sentences of \(L\), \(\{\theta_1, \ldots \theta_m\}\) with probabilities \(\{\eta_1, \ldots, \eta_m\}\), \((\vec{e},\zeta)\)-entails \(\psi\) provided that the probability of \(\psi\) is at least \(\zeta\) for all probability functions \(P\) for which \(P ...
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2011
We define an extension of stit logic that encompasses subjective probabilities representing beliefs about simultaneous choice exertion of other agents. This semantics enables us to express that an agent sees to it that a condition obtains under a minimal chance of success.
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We define an extension of stit logic that encompasses subjective probabilities representing beliefs about simultaneous choice exertion of other agents. This semantics enables us to express that an agent sees to it that a condition obtains under a minimal chance of success.
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Nanocomputing with Probabilistic Logic
2006 Sixth IEEE Conference on Nanotechnology, 2006This presentation considers the impact on logic design and computing of the fundamental unreliability of nanoscale device technologies. In general, these technologies will provide implementations of logic gates and circuits where logic levels are “0” or “1” with some probability related to the error rates of gates and interconnect.
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