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Deductive Systems in Traditional and Modern Logic

Deductive Systems in Traditional and Modern Logic

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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.

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Keywords

  • (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
  • Leśniewski’s elementary ontology
  • Lewis Carroll
  • logic
  • Logic diagrams
  • logic of determination of objects (LDO)
  • logic of typical and atypical instances (LTA)
  • logic trees
  • logics of evidence and truth
  • Mathematics & 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 & interdisciplinary subjects
  • refutation systems
  • rejection systems
  • Research & 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

Links

DOI: 10.3390/books978-3-03943-359-9

Editions

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