Deductive Systems in Traditional and Modern Logic

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quine; logic; ontology; multiple conclusion rule; disjunction property; metadisjunction; axiomatizations of arithmetic of natural and integers numbers; second-order theories; Peano’s axioms; Wilkosz’s axioms; axioms of integer arithmetic modeled on Peano and Wilkosz axioms; equivalent axiomatizations; metalogic; categoricity; independence; consistency; logic of typical and atypical instances (LTA); logic of determination of objects (LDO); quasi topology structure (QTS); concept; object; typical object; atypical object; lattice; filter; ideal; discussive logics; the smallest discussive logic; discussive operators; seriality; accessibility relation; Kotas’ method; modal logic; deontic logic; ontology of situations; semantics of law; formal theory of law; Wittgenstein; Wolniewicz; non-Fregean logic; identity connective; sentential calculus with identity; situational semantics; deduction; (dual) tableau; Gentzen system; deductive refutability; refutation systems; hybrid deduction–refutation rules; derivative hybrid rules; soundness; completeness; natural deduction; meta-proof theory; synthetic tableaux; principle of bivalence; cut; first-order theory; universal axiom; Peano’s axiomatics of natural numbers; Leśniewski’s elementary ontology; Frege’s predication scheme; Frege’s Zahl-Anzahl distinction; term logic; Franz Brentano; Lewis Carroll; logic trees; logic diagrams; paraconsistent logic; paraconsistency; Sette’s calculus; the law of explosion; the principle of ex contradictione sequitur quodlibet; semantic tree; term logic; distribution; Aristotle’s logic; syllogistic; Jan Łukasiewicz; axiomatic system; axiomatic refutation; completeness; temporal logic; intuitionistic logic; minimal system; knowledge; sequent-type calculi; nonmonotonic logics; default logic; rejection systems; Kripke models; logics of evidence and truth; paraconsistency; n/a