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style = "sciml" |
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freebsd_instance: | ||
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task: | ||
name: FreeBSD | ||
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```@meta | ||
CurrentModule = SoleLogics.ManyValuedLogics | ||
``` | ||
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```@contents | ||
Pages = ["many-valued-logics.md"] | ||
``` | ||
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# [Introduction](@id many-valued-logics-introduction) | ||
SoleLogics also provides tools to work with [many-valued logics](https://en.wikipedia.org/wiki/Many-valued_logic) (e.g., fuzzy logics), that is, logics with more truth values other than the classical Boolean ones `⊤` and `⊥`. With many-valued logics, the truth values are elements of a bounded lattice, providing a partial order between them, which encodes a *truer than* relation. | ||
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Most of the tools for dealing with these logics can be accessed by importing the ManyValuedLogics submodule: | ||
```julia | ||
using SoleLogics.ManyValuedLogics | ||
``` | ||
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# [Operation](@id many-valued-logics-operation) | ||
```@docs | ||
Operation | ||
BinaryOperation | ||
``` | ||
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# [Axiom](@id many-valued-logics-axiom) | ||
```@docs | ||
Axiom | ||
checkaxiom | ||
``` | ||
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## [Common axioms](@id many-valued-logics-common-axioms) | ||
```@docs | ||
Commutativity | ||
Associativity | ||
AbsorptionLaw | ||
LeftIdentity | ||
RightIdentity | ||
IdentityElement | ||
RightResidual | ||
LeftResidual | ||
ResiduationProperty | ||
Implication1 | ||
Implication2 | ||
Implication3 | ||
DistributiveLaw | ||
``` | ||
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# [Finite algebra](@id many-valued-logics-finite-algebra) | ||
```@docs | ||
FiniteAlgebra | ||
``` | ||
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## [Monoid](@id many-valued-logics-monoid) | ||
```@docs | ||
Monoid | ||
CommutativeMonoid | ||
``` | ||
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## [Finite lattice](@id many-valued-logics-finite-lattice) | ||
```@docs | ||
FiniteLattice | ||
FiniteBoundedLattice | ||
FiniteResiduatedLattice | ||
``` | ||
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## [Finite algebra varieties](@id many-valued-logics-finite-algebra-varieties) | ||
```@docs | ||
FiniteFLewAlgebra | ||
FiniteHeytingAlgebra | ||
``` | ||
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# [Order utilities](@id many-valued-logics-order-utilities) | ||
```@docs | ||
precedeq | ||
precedes | ||
succeedeq | ||
succeedes | ||
``` |
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