The conditional implication is interpreted as causal implication.
Furthermore, an analysis of truth in fiction in terms of some modal notion (whether a counterfactual conditional, strict implication, or whatever) would not make the account circular, since analysing modal discourse would be no part of the purpose of the fictional machinery.
Lewis also shows that contraposition, the implication of ~q □→ ~p by p □→ q, and conditional syllogism, the implication of p □→ r by p □→ q and q □→ r, are invalid on his model, and gives arguments that they should be considered invalid.
We introduce a lattice-theoretic framework that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures.
The Philonian conditional resembles material implication, except that—since propositions were conceived of as functions of time that can have different truth-values at different times it may change its truth-value over time.
Conditional statements IF….THEN rules (implication, deduction) are the things that make fuzzy logic useful.
I believe the authors need to add further explanation as to the implications of conditional Ka/Ks because of the following: In table 1, several of the Codon X's are actually known to follow the Codon Y. Therefore the statistical dependence of Y on X, does not necessarily mean that Y follows X.
This is different from the traditional view of logic, in which the conditional has a material implication truth table, in which the conditional is true for these three cases and just false for p not q cases.
He also notes that his preferred counterfactual logic invalidates several familiar implications involving conditionals.
If the predicate 'is a heap' denotes a fuzzy set and the conditional is interpreted as implication in Łukasiewicz's continuum-valued logic, then the Sorites Paradox can be avoided.
