3 and 4. In Sect. 3 we introduced the notions of logical entropy and logical conditional entropy of finite measurable partitions of a probability space and we examined basic properties of the proposed measures.
The monotonicity of probability measure μ implies the inequality (mu(A_{i} cap B_{j}) lemu(B_{j})), so it is evident that the logical conditional entropy (H_{L} ( alpha/beta )) is a nonnegative number.
If (alpha= { A_{1},A_{2},ldots,A_{n} }) and (beta= { B_{1},B_{2},ldots,B_{m} }) are two partitions of Ω, then the logical conditional entropy of α assuming a realization of the experiment β is defined as the number H_{L} ( alpha/beta )= sum_{i = 1}^{n} sum_{j = 1}^{m} mu (A_{i} cap B_{j}) bigl(mu(B_{j}) - mu(A_{i} cap B_{j} bigr).
Logical conditional operators, such as AND gates based on conformation switching, could be used to locally determine if assembly is appropriate and permitted.
It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitative possibilistic logic are all sublogics of the presented logical framework.
The effect of two instructional variables, visualisation and manipulation of objects, in learning to use the logical connective, conditional, was investigated.
Using binary variables, qualitative biological knowledge such as logical or conditional relationships or temporally uncertain data can be specified and considered (Rumschinski et al., 2012).
In some cases we have positive arguments, like the one advanced by Alan Gibbard in (1981), that an entire (grammatical or logical) class of conditionals does not carry truth values (indicative conditionals in the case of Gibbard).
The problem with this reading is that it offers no more than what any conditional logical proof can offer support for the conditional in question when what one really seeks is support for the antecedent as well.
Both inferences are valid for strict (logical or material) conditionals, but they are not generally correct for non-strict conditionals.
