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Reasoning in Infinitely Valued G-IALCQ

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Stefan Borgwardt, Rafael Peñaloza

Artificial Intelligence · Submitted 29 Sep 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions.

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arXiv ID1509.08761 (version 1)
Pith IDCKJV5VQW, Pith's permanent record of this paper and its review
CitationRafael Pe\~naloza, Stefan Borgwardt. "Reasoning in Infinitely Valued G-IALCQ." arXiv:1509.08761 (2015). https://pith.science/paper/CKJV5VQW
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,912 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.93 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable in the presence of a negation constructor and general concept inclusion axioms. One exception to this negative result are FDLs whose semantics is based on the infinitely valued G\"odel t-norm (G). In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and the automata-based procedure originally developed for reasoning in G-IALC. The proposed approach combines the advantages of these two methods, while removing their respective drawbacks.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. background 1.00 0.05 0.02 asserted 1.00
s1 It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable in the presence of a negation constructor and general concept inclusion axioms. background 0.99 0.05 0.03 asserted 1.00
s2 One exception to this negative result are FDLs whose semantics is based on the infinitely valued G\"odel t-norm (G). background 0.97 0.05 0.05 asserted 1.00
s3 In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions. contribution 0.99 0.89 0.42 asserted 0.99
s4 Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and the automata-based procedure originally developed for reasoning in G-IALC. method 0.97 0.84 0.10 asserted 1.00
s5 The proposed approach combines the advantages of these two methods, while removing their respective drawbacks. interpretation 0.72 0.72 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.85 · evidence from proof or derivation 0.94.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable in the presence of a negation constructor and general concept inclusion axioms. One exception to this negative result are FDLs whose semantics is based on the infinitely valued G\"odel t-norm (G). In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and the automata-based procedure originally developed for reasoning in G-IALC. The proposed approach combines the advantages of these two methods, while removing their respective drawbacks.

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