logics - MathStructures

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=====Logics=====

This page is intended to contain an alphabetical list of propositional and predicate logics that have been investigated in the published literature.

This list is still **very much under construction**, so feel free to add further logics, and to add information about individual entries.

Many of the propositional logics on this page have algebraic semantics given by a class of structures on the [[http://math.chapman.edu/~jipsen/structures/doku.php/|main page]]. Algebraic logic is the area that investigates the connections between logics and their algebraic counterparts.

  -[[Arrow logic]]
  -[[Basic logic]]
  -[[BCI logic]]
  -[[BCK logic]]
  -[[Classical full Lambek calculus]]
  -[[Classical propositional logic]]
  -[[Classical predicate logic]]
  -[[Classical predicate logic|First order logic]]
  -[[Full Lambek calculus]]
  -[[Full Lambek calculus with contraction]]
  -[[Full Lambek calculus with exchange]]
  -[[Full Lambek calculus with weakening]]
  -[[Goedel logic]]
  -[[Intuitionistic logic]]
  -[[Intuitionistic multiplicative additive linear logic]]
  -[[Linear logic]]
  -[[Lukasiewicz logic]]
  -[[Modal logic K]]
  -[[Modal logic T]]
  -[[Modal logic S4]]
  -[[Modal logic S5]]
  -[[Multiplicative additive linear logic]]
  -[[Lukasiewicz logic|Multivalued logic]]
  -[[Orthologic]]
  -[[Quantum computational logic]]
  -[[Quantum logic]]
  -[[Positive modal logic]]
  -[[Product logic]]
  -[[Relevance logic]]
  -[[Substructural logic]]
  -[[Temporal logic]]
  -[[Tense logic]]

Trace: • semigroups • commutative_rings • semirings_with_identity_and_zero • quantales • priestley_spaces • finite_commutative_binars_with_zero • abelian_partially_ordered_groups • first-order_formulas • semirings_with_zero