If he has in mind the standard notion of logical implication (truth preservation on every domain and interpretation of the nonlogical constants), then (2) is false: \(\dq{\#\neg(0=0) \vee \neg(0=0)}\) is true on every interpretation, but "water = H2O" is false on many interpretations (those that assign distinct referents to the nonlogical constants "water" and "H2O").
This is especially true for the notions of set and collection in general, for the basic syntactical and semantical concepts of standard classical logic (logical languages of a given order, the notion of satisfiability, definability).
On the one hand, information underlies the intuitive understanding of standard logical notions such as inference (commonly thought of as the process that turns implicit information into explicit one) and computation.
First of all, anyone who wants to maintain some kind of indeterminism regarding the future, may be confronted with some standard arguments in favor of logical determinism, i.e., arguments designed to demonstrate that there are no future contingents at all.
After a brief statement of standard logical approaches to consequence, we describe motivations for new systems.
In this paper, we report on the SBML Level 3 Qualitative Model (SBML qual) package, which provides a standard means for the exchange of logical models of regulatory and signalling networks.
In the case of propositional logic, a standard view is that the meaning of logical connectives such as conjunction is given by a truth table, which shows how the truth or falsity of a compound sentence is determined by the truth values of its component sentences.
A standard approach to the mathematical characterization of logical truth, alternative to the derivability approach, uses always some version of the property of universal validity, proposing it in each case as both necessary and sufficient for logical truth.
This scheme of sentences is the standard logical form of AC. is the direct counterpart of AC1 in this strengthened second-order language.
