Displaying similar documents to “On some inexact relations in probabilized Boolean algebras.”

Modus ponens on Boolean algebras revisited.

Enric Trillas, Susana Cubillo (1996)

Mathware and Soft Computing

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In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.

Didactical note: probabilistic conditionality in a Boolean algebra.

Enric Trillas, Claudi Alsina, Settimo Termini (1996)

Mathware and Soft Computing

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This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem...

Considering uncertainty and dependence in Boolean, quantum and fuzzy logics

Mirko Navara, Pavel Pták (1998)

Kybernetika

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A degree of probabilistic dependence is introduced in the classical logic using the Frank family of t -norms known from fuzzy logics. In the quantum logic a degree of quantum dependence is added corresponding to the level of noncompatibility. Further, in the case of the fuzzy logic with P -states, (resp. T -states) the consideration turned out to be fully analogous to (resp. considerably different from) the classical situation.

On MPT-implication functions for fuzzy logic.

Enric Trillas, Claudi Alsina, Ana Pradera (2004)

RACSAM

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This paper deals with numerical functions J : [0,1] x [0,1] → [0,1] able to functionally express operators →: [0,1] x [0,1] → [0,1] defined as (μ → σ)(x,y) = J(μ(x),σ(y)), and verifying either Modus Ponens or Modus Tollens, or both. The concrete goal of the paper is to search for continuous t-norms T and strong-negation functions N for which it is either T(a, J(a,b)) ≤ b (Modus Ponens) or T(N(b), J(a,b)) ≤ N(a) (Modus Tollens), or both, for all a,b in [0,1] and a given J. Functions J...