166,190 research outputs found
Quantum Team Logic and Bell's Inequalities
A logical approach to Bell's Inequalities of quantum mechanics has been
introduced by Abramsky and Hardy [2]. We point out that the logical Bell's
Inequalities of [2] are provable in the probability logic of Fagin, Halpern and
Megiddo [4]. Since it is now considered empirically established that quantum
mechanics violates Bell's Inequalities, we introduce a modified probability
logic, that we call quantum team logic, in which Bell's Inequalities are not
provable, and prove a Completeness Theorem for this logic. For this end we
generalise the team semantics of dependence logic [7] first to probabilistic
team semantics, and then to what we call quantum team semantics
Fuzzy inequational logic
We present a logic for reasoning about graded inequalities which generalizes
the ordinary inequational logic used in universal algebra. The logic deals with
atomic predicate formulas of the form of inequalities between terms and
formalizes their semantic entailment and provability in graded setting which
allows to draw partially true conclusions from partially true assumptions. We
follow the Pavelka approach and define general degrees of semantic entailment
and provability using complete residuated lattices as structures of truth
degrees. We prove the logic is Pavelka-style complete. Furthermore, we present
a logic for reasoning about graded if-then rules which is obtained as
particular case of the general result
Possible Experience: from Boole to Bell
Mainstream interpretations of quantum theory maintain that violations of the
Bell inequalities deny at least either realism or Einstein locality. Here we
investigate the premises of the Bell-type inequalities by returning to earlier
inequalities presented by Boole and the findings of Vorob'ev as related to
these inequalities. These findings together with a space-time generalization of
Boole's elements of logic lead us to a completely transparent Einstein local
counterexample from everyday life that violates certain variations of the Bell
inequalities. We show that the counterexample suggests an interpretation of the
Born rule as a pre-measure of probability that can be transformed into a
Kolmogorov probability measure by certain Einstein local space-time
characterizations of the involved random variables.Comment: Published in: EPL, 87 (2009) 6000
About Nonstandard Neutrosophic Logic (Answers to Imamura 'Note on the Definition of Neutrosophic Logic')
In order to more accurately situate and fit the neutrosophic logic into the
framework of nonstandard analysis, we present the neutrosophic inequalities,
neutrosophic equality, neutrosophic infimum and supremum, neutrosophic standard
intervals, including the cases when the neutrosophic logic standard and
nonstandard components T, I, F get values outside of the classical real unit
interval [0, 1], and a brief evolution of neutrosophic operators. The paper
intends to answer Imamura criticism that we found benefic in better
understanding the nonstandard neutrosophic logic, although the nonstandard
neutrosophic logic was never used in practical applications.Comment: 16 page
Reasoning with global assumptions in arithmetic modal logics
We establish a generic upper bound ExpTime for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the in- stance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning
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