Multi-adjoint logic programming

Short description: Sub-field of 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.

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. 2173. 351–364. doi:10.1007/3-540-45402-0_26. ISBN 978-3-540-42593-9.
2. ↑ "Rfuzzy". http://babel.ls.fi.upm.es/software/rfuzzy/.
3. ↑ "Floper". http://dectau.uclm.es/floper/.

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