A Tabulation Proof Procedure for First-order Residuated Logic Programs: Soundness, Completeness and Optimizations

 

Abstract

Residuated logic programs have shown to be a generalisation of a number of approaches to logic programming under uncertain or vague information, including fuzzy or annotated or probabilistic or similarity-based logic programming frameworks. Various computational approaches have been developed for propositional residuated logic programs: on the one hand, there exists a bottom-up neural-like implementation of the fixed-point semantics which calculates the successive iterations of the immediate consequences operator; on the other hand, a goal-oriented top-down tabulation procedure has recently been introduced. In this paper, we introduce a sound and complete tabulation-based proof procedure for the first-order extension of residuated logic programs.

Citation

Please, cite this work as:

[DMO06] C. V. Damásio, J. Medina, and M. Ojeda-Aciego. “A Tabulation Proof Procedure for First-order Residuated Logic Programs: Soundness, Completeness and Optimizations”. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2006, Vancouver, BC, Canada, July 16-21, 2006. IEEE, 2006, pp. 2004-2011. DOI: 10.1109/FUZZY.2006.1681978. URL: https://doi.org/10.1109/FUZZY.2006.1681978.

BibTeX

@InProceedings{Damasio2006,
     author = {Carlos Viegas Dam{’a}sio and Jes{’u}s Medina and Manuel Ojeda-Aciego},
     booktitle = {{IEEE} International Conference on Fuzzy Systems, {FUZZ-IEEE} 2006, Vancouver, BC, Canada, July 16-21, 2006},
     title = {A Tabulation Proof Procedure for First-order Residuated Logic Programs: Soundness, Completeness and Optimizations},
     year = {2006},
     pages = {2004–2011},
     publisher = {{IEEE}},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/conf/fuzzIEEE/DamasioMO06.bib},
     doi = {10.1109/FUZZY.2006.1681978},
     timestamp = {Thu, 07 Jan 2021 00:00:00 +0100},
     url = {https://doi.org/10.1109/FUZZY.2006.1681978},
}

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A Tabulation Proof Procedure for First-order Residuated Logic Programs: Soundness, Completeness and Optimizations

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] A. Chortaras, G. Stamou, and A. Stafylopatis. “Integrated Query Answering with Weighted Fuzzy Rules”. In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Springer Berlin Heidelberg, 2007, p. 767–778. ISBN: 9783540752561. DOI: 10.1007/978-3-540-75256-1_67. URL: http://dx.doi.org/10.1007/978-3-540-75256-1_67.

[2] C. Damasio, J. Medina, and M. Ojeda-Aciego. “A Tabulation Proof Procedure for First-order Residuated Logic Programs: Soundness, Completeness and Optimizations”. In: 2006 IEEE International Conference on Fuzzy Systems. IEEE, 2006, p. 2004–2011. DOI: 10.1109/fuzzy.2006.1681978. URL: http://dx.doi.org/10.1109/fuzzy.2006.1681978.

[3] C. Damasio, J. Pan, G. Stoilos, et al. “An Approach to Representing Uncertainty Rules in RuleML”. In: 2006 Second International Conference on Rules and Rule Markup Languages for the Semantic Web (RuleML’06). IEEE, Nov. 2006, p. 97–106. DOI: 10.1109/ruleml.2006.3. URL: http://dx.doi.org/10.1109/ruleml.2006.3.

[4] P. Julián-Iranzo, J. Medina, and M. Ojeda-Aciego. “On reductants in the framework of multi-adjoint logic programming”. In: Fuzzy Sets and Systems 317 (Jun. 2017), p. 27–43. ISSN: 0165-0114. DOI: 10.1016/j.fss.2016.09.004. URL: http://dx.doi.org/10.1016/j.fss.2016.09.004.

[5] P. Julián-Iranzo, G. Moreno, and J. A. Riaza. “The Fuzzy Logic Programming language FASILL: Design and implementation”. In: International Journal of Approximate Reasoning 125 (Oct. 2020), p. 139–168. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2020.06.002. URL: http://dx.doi.org/10.1016/j.ijar.2020.06.002.

[6] V. H. Le. “Efficient Query Answering for Fuzzy Linguistic Logic Programming”. In: 2012 IEEE RIVF International Conference on Computing & Communication Technologies, Research, Innovation, and Vision for the Future. IEEE, Feb. 2012, p. 1–4. DOI: 10.1109/rivf.2012.6169836. URL: http://dx.doi.org/10.1109/rivf.2012.6169836.

[7] V. H. Le and F. Liu. “Tabulation proof procedures for fuzzy linguistic logic programming”. In: International Journal of Approximate Reasoning 63 (Aug. 2015), p. 62–88. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2015.06.001. URL: http://dx.doi.org/10.1016/j.ijar.2015.06.001.

[8] Y. Loyer and U. Straccia. “Approximate well-founded semantics, query answering and generalized normal logic programs over lattices”. In: Annals of Mathematics and Artificial Intelligence 55.3–4 (Oct. 2008), p. 389–417. ISSN: 1573-7470. DOI: 10.1007/s10472-008-9099-0. URL: http://dx.doi.org/10.1007/s10472-008-9099-0.

[9] U. Straccia. “Managing Uncertainty and Vagueness in Description Logics, Logic Programs and Description Logic Programs”. In: Reasoning Web. Springer Berlin Heidelberg, 2008, p. 54–103. ISBN: 9783540856580. DOI: 10.1007/978-3-540-85658-0_2. URL: http://dx.doi.org/10.1007/978-3-540-85658-0_2.

[10] U. Straccia. “On the Top-k Retrieval Problem for Ontology-Based Access to Databases”. In: Flexible Approaches in Data, Information and Knowledge Management. Springer International Publishing, Sep. 2013, p. 95–114. ISBN: 9783319009544. DOI: 10.1007/978-3-319-00954-4_5. URL: http://dx.doi.org/10.1007/978-3-319-00954-4_5.

[11] U. Straccia and F. Bobillo. “From Fuzzy to Annotated Semantic Web Languages”. In: Reasoning Web: Logical Foundation of Knowledge Graph Construction and Query Answering. Springer International Publishing, 2017, p. 203–240. ISBN: 9783319494937. DOI: 10.1007/978-3-319-49493-7_6. URL: http://dx.doi.org/10.1007/978-3-319-49493-7_6.