fosf - Fuzzy OSF Logic in Python

These pages contain the documentation for fosf, a Python implementation of the main reasoning algorithms of (fuzzy) order-sorted feature (OSF) logic [1] [3]. In particular, fosf supports the following operations.

• (Fuzzy) OSF taxonomic reasoning: computing greatest lower bounds (GLBs) of sorts, deciding sort subsumption, computing sort subsumption degrees, computing membership degrees of instances with respect to sorts.

• OSF clause and term normalization: simplifying a given OSF clause or term into a normal form.

• (Fuzzy) OSF term unification: unifying two (normal) OSF terms to compute their GLB in the (fuzzy) OSF term subsumption lattice, and computing the subsumption degree of the unifier with respect to the initial terms.

• (Fuzzy) OSF term normalization with respect to an OSF theory: Normalize an OSF term according to the structural constraints imposed by sort definitions [2], and computing the satisfaction degree of a term with respect to the OSF theory.

Below you can find an example of how to use fosf, the API reference, and the EBNF grammar reference for parsing OSF syntax.

Contents:

• Example - Fuzzy OSF Logic with fosf
  • Fuzzy sort taxonomies
  • OSF constraints and clauses
  • OSF constraint normalization
  • OSF Terms
  • OSF term normalization
  • Fuzzy OSF term unification
  • Sort definitions
• API Reference
  • Syntax
  • Reasoning
  • Parsers
• EBNF grammars for parsing OSF structures
  • Base OSF Grammar
  • Graph Grammar
  • Taxonomy Grammar
  • OSF Term Grammar
  • OSF Clause Grammar
  • OSF Theory Grammar

Indices

• Index

• Module Index

References

[1]

Hassan Aït-Kaci and Andreas Podelski. Towards a meaning of life. J. Log. Program., 16(3):195–234, 1993. doi:https://doi.org/10.1016/0743-1066(93)90043-G.

[2]

Hassan Aït-Kaci, Andreas Podelski, and Seth Copen Goldstein. Order-sorted feature theory unification. The Journal of Logic Programming, 30(2):99–124, 1997. doi:https://doi.org/10.1016/S0743-1066(96)00053-2.

[3]

Gian Carlo Milanese and Gabriella Pasi. Fuzzy order-sorted feature logic. Fuzzy Sets and Systems, 477:108800, 2024. doi:https://doi.org/10.1016/j.fss.2023.108800.