تقرير
Non-standard modalities in paraconsistent G\'{o}del logic
| العنوان: | Non-standard modalities in paraconsistent G\'{o}del logic |
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| المؤلفون: | Bilkova, Marta, Frittella, Sabine, Kozhemiachenko, Daniil |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Logic |
| الوصف: | We introduce a paraconsistent expansion of the G\"{o}del logic with a De Morgan negation $\neg$ and modalities $\blacksquare$ and $\blacklozenge$. We equip it with Kripke semantics on frames with two (possibly fuzzy) relations: $R^+$ and $R^-$ (interpreted as the degree of trust in affirmations and denials by a given source) and valuations $v_1$ and $v_2$ (positive and negative support) ranging over $[0,1]$ and connected via $\neg$. We motivate the semantics of $\blacksquare\phi$ (resp., $\blacklozenge\phi$) as infima (suprema) of both positive and negative supports of $\phi$ in $R^+$- and $R^-$-accessible states, respectively. We then prove several instructive semantical properties of the logic. Finally, we devise a tableaux system for branching fragment and establish the complexity of satisfiability and validity. Comment: arXiv admin note: text overlap with arXiv:2303.14164 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/978-3-031-43619-2_29 |
| الوصول الحر: | http://arxiv.org/abs/2303.14198Test |
| رقم الانضمام: | edsarx.2303.14198 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/978-3-031-43619-2_29 |
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