Deductive Systems in Traditional and Modern Logic

• Format: eBook
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: (dual) tableau; accessibility relation; Aristotle’s logic; atypical object; axiomatic refutation; axiomatic system; axiomatizations of arithmetic of natural and integers numbers; axioms of integer arithmetic modeled on Peano and Wilkosz axioms; categoricity; completeness; concept; consistency; cut; deduction; deductive refutability; default logic; deontic logic; derivative hybrid rules; discussive logics; discussive operators; disjunction property; distribution; equivalent axiomatizations; filter; first-order theory; formal theory of law; Franz Brentano; Frege’s predication scheme; Frege’s Zahl-Anzahl distinction; Gentzen system; hybrid deduction–refutation rules; ideal; identity connective; independence; intuitionistic logic; Jan Łukasiewicz; knowledge; Kotas’ method; Kripke models; lattice; Lewis Carroll; Leśniewski’s elementary ontology; logic; logic diagrams; logic of determination of objects (LDO); logic of typical and atypical instances (LTA); logic trees; logics of evidence and truth; Mathematics and Science; meta-proof theory; metadisjunction; metalogic; minimal system; modal logic; multiple conclusion rule; n/a; natural deduction; non-Fregean logic; nonmonotonic logics; object; ontology; ontology of situations; paraconsistency; paraconsistent logic; Peano’s axiomatics of natural numbers; Peano’s axioms; principle of bivalence; quasi topology structure (QTS); quine; Reference, Information and Interdisciplinary subjects; refutation systems; rejection systems; Research and information: general; second-order theories; semantic tree; semantics of law; sentential calculus with identity; sequent-type calculi; seriality; Sette’s calculus; situational semantics; soundness; syllogistic; synthetic tableaux; temporal logic; term logic; the law of explosion; the principle of ex contradictione sequitur quodlibet; the smallest discussive logic; typical object; universal axiom; Wilkosz’s axioms; Wittgenstein; Wolniewicz
• ISBN: 9783039433599; 3039433598; 303943358X; 9783039433582
• DOI: 10.3390/books978-3-03943-359-9

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic.