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FIRST-ORDER RELEVANT REASONERS IN CLASSICAL WORLDS

Part of: General logic

Published online by Cambridge University Press:  21 March 2023

NICHOLAS FERENZ
NICHOLAS FERENZ*
Affiliation:
INSTITUTE OF COMPUTER SCIENCE CZECH ACADEMY OF SCIENCES 182 00 PRAHA 8, CZECH REPUBLIC
*
E-mail: ferenz@cs.cas.cz
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Abstract

Sedlár and Vigiani [18] have developed an approach to propositional epistemic logics wherein (i) an agent’s beliefs are closed under relevant implication and (ii) the agent is located in a classical possible world (i.e., the non-modal fragment is classical). Here I construct first-order extensions of these logics using the non-Tarskian interpretation of the quantifiers introduced by Mares and Goldblatt [12], and later extended to quantified modal relevant logics by Ferenz [6]. Modular soundness and completeness are proved for constant domain semantics, using non-general frames with Mares–Goldblatt truth conditions. I further detail the relation between the demand that classical possible worlds have Tarskian truth conditions and incompleteness results in quantified relevant logics.

Keywords

relevant logicepistemic logicnon-Tarskian quantifiersfirst-order epistemic logic

MSC classification

Primary: 03B10: Classical first-order logic 03B42: Logics of knowledge and belief (including belief change) 03B45: Modal logic (including the logic of norms) 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
Type
Research Article
Information
The Review of Symbolic Logic , First View , pp. 1 - 26
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

BIBLIOGRAPHY

Anderson, A. R., Belnap, N. D., & Dunn, J. M. (1992). Entailment: The Logic of Relevance and Necessity, Vol. 2. Princeton: Princeton University Press.Google Scholar
Bílková, M., Majer, O., & Peliš, M. (2016). Epistemic logics for sceptical agents. Journal of Logic and Computation, 26, 1815–1841.CrossRefGoogle Scholar
Bílková, M., Majer, O., Peliš, M., & Restall, G. (2010). Relevant agents. Advances in Modal Logic, 8, 22–38.Google Scholar
Ferenz, N. (2021). Identity in Relevant Logics: A Relevant Predicative Approach. The Logica Yearbook 2020. London: College Publications, pp. 49–64.Google Scholar
Ferenz, N. (2020). Quantified Modal Relevant Logics. Ph.D. Thesis, University of Alberta, Edmonton.Google Scholar
Ferenz, N. (2023). Quantified modal relevant logics. Review of Symbolic Logic, 16, 210–240.CrossRefGoogle Scholar
Fine, K. (1989). Incompleteness for quantified relevant logics. In Norman, J., and Sylvan, R., editors. Directions in Relevant Logic. New York: Kluwer Academic Publishers, pp. 205–225. Reprinted in [1], Vol. 2, §52.CrossRefGoogle Scholar
Goldblatt, R. (2011). Quantifiers, Propositions and Identity. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Goldblatt, R., & Mares, E. (2006). A general semantics for quantified modal logic. Advances in Modal Logic, 6, 227–246.Google Scholar
Kremer, P. (1999). Relevant identity. Journal of Philosophical Logic, 28, 199–222.CrossRefGoogle Scholar
Mares, E. (2009). General information in relevant logic. Synthese, 167, 343–362.CrossRefGoogle Scholar
Mares, E., & Goldblatt, R. (2006). An alternative semantics for quantified relevant logic. Journal of Symbolic Logic, 71, 163–187.CrossRefGoogle Scholar
Mares, E., & Meyer, R. K. (1993). The semantics of R4 . Journal of Philosophical Logic, 22, 95–110.CrossRefGoogle Scholar
Meyer, R. K. (1981). Almost Skolem forms for relevant (and other) logics. Logique et Analyse, NOUVELLE SÉRIE, 24, 277–289.Google Scholar
Restall, G. (2002). An Introduction to Substructural Logics. London: Routledge.CrossRefGoogle Scholar
Routley, R., Plumwood, V., Meyer, R. K., & Brady, R. T. (1982). Relevant Logics and Their Rivals: Part 1 the Basic Philosophical and Semantical Theory. Ridgewood: Ridgeview Publishing Company.Google Scholar
Sedlár, I. (2015). Substructural epistemic logics. Journal of Applied Non-Classical Logics, 25, 256–285.CrossRefGoogle Scholar
Sedlár, I., & Vigiani, P. (2022). Relevant reasoners in a classical world. In Fernández-Duque, D., Palmigiano, A., and Pinchinat, S., editors. Proceedings of the 14th International Conference on Advances in Modal Logic (AiML 2022). London: College Publications, pp. 697–718.Google Scholar
Segerber, K. (1971). An Essay in Classical Modal Logic. Ph.D. Thesis, Stanford University, Stanford.Google Scholar
Seki, T. (2003). General frames for relevant modal logics. Notre Dame Journal of Formal Logic, 44, 93–109.CrossRefGoogle Scholar
Seki, T. (2003). A Sahlqvist theorem for relevant modal logics. Studia Logica, 73, 383–411.CrossRefGoogle Scholar
Standefer, S. (2021). Identity in Mares-Goldblatt models for quantified relevant logic. Journal of Philosophical Logic, 50, 1389–1415.CrossRefGoogle Scholar
Syverson, P. (2003). Logic, Convention, and Common Knowledge: A Conventionalist Account of Logic. Stanford: CSLI Publications.Google Scholar
Tedder, A., & Ferenz, N. (2022). Neighbourhood semantics for quantified relevant logics. Journal of Philosophical Logic, 51, 457–484.CrossRefGoogle Scholar