Multi-adjoint logic programming

Multi-adjoint logic programming^[1] defines syntax and semantics of a logic programming program in such a way that the underlying maths justifying the results are a residuated lattice and/or MV-algebra.

The definition of a multi-adjoint logic program is given, as usual in fuzzy logic programming, as a set of weighted rules and facts of a given formal language F. Notice that we are allowed to use different implications in our rules.

Definition: A multi-adjoint logic program is a set P of rules of the form <(A ←i B), δ> such that:

1. The rule (A ←i B) is a formula of F;

2. The confidence factor δ is an element (a truth-value) of L;

3. The head A is an atom;

4. The body B is a formula built from atoms B1, …, Bn (n ≥ 0) by the use of conjunctors, disjunctors, and aggregators.

5. Facts are rules with body ┬.

6. A query (or goal) is an atom intended as a question ?A prompting the system.

Implementations

Implementations of Multi-adjoint logic programming: Rfuzzy,^[2] Floper,^[3] and more we do not remember now.

References

^ Medina, Jesús; Ojeda-Aciego, Manuel; Vojtaš, Peter (2001). "Multi-adjoint Logic Programming with Continous Semantics". Logic Programming and Nonmotonic Reasoning. Lecture Notes in Computer Science. Vol. 2173. pp. 351–364. doi:10.1007/3-540-45402-0_26. ISBN 978-3-540-42593-9. {{cite book}}: |journal= ignored (help)
^ "Rfuzzy". Archived from the original on 2012-02-28. Retrieved 2012-01-21.
^ "Floper".

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[1] Medina, Jesús; Ojeda-Aciego, Manuel; Vojtaš, Peter (2001). "Multi-adjoint Logic Programming with Continous Semantics". Logic Programming and Nonmotonic Reasoning. Lecture Notes in Computer Science. Vol. 2173. pp. 351–364. doi:10.1007/3-540-45402-0_26. ISBN 978-3-540-42593-9. {{cite book}}: |journal= ignored (help)

[2] "Rfuzzy". Archived from the original on 2012-02-28. Retrieved 2012-01-21.

[3] "Floper".

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