Implicational partial Galois logics and some of their semilinear extensions, such as extensions satisfying abstract dual connection properties, have been introduced together with relational semantics. However, similar residuated, residuated properties not. This paper fills the gaps by introducing those To this end, class implicational (dual) residuated-connected prelinear gaggle is defined it v...

Completion is a general paradigm for applying inferences to generate a canonical presentation of a logical theory, or to semi-decide the validity of theorems, or to answer queries. We investigate what canonicity means for implicational systems that are axiomatizations of Moore families – or, equivalently, of propositional Horn theories. We build a correspondence between implicational systems an...

The core of our argument is that the human mental architecture is composed of nine subsystems of equal status that interact as parts of a coherent overall system, and therefore one mind. Two of these subsystems represent qualitatively different types of meaning, one propositional in nature and the other a more abstract holistic representation, called implicational meaning (Barnard & Teasdale, 1...

An equivalence is shown between functional dependency statements of a relational database, where “+” has the meaning of “determines,” and implicational statements of propositional logic, where “.$” has the meaning of “implies.” Specifically, it is shown that a dependency statement is a consequence of a set of dependency statements iff the corresponding implicational statement is a consequence o...