Epistemic Syllogistic: First Steps (2307.05043v1)
Abstract: Aristotle's discussions on modal syllogistic have often been viewed as error-prone and have garnered significant attention in the literature due to historical and philosophical interests. However, from a contemporary standpoint, they also introduced natural fragments of first-order modal logic, warranting a comprehensive technical analysis. In this paper, drawing inspiration from the natural logic program, we propose and examine several variants of modal syllogistic within the epistemic context, thereby coining the term Epistemic Syllogistic. Specifically, we concentrate on the de re interpretation of epistemic syllogisms containing non-trivial yet natural expressions such as "all things known to be A are also known to be not B." We explore the epistemic apodeictic syllogistic and its extensions, which accommodate more complex terms. Our main contributions include several axiomatizations of these logics, with completeness proofs that may be of independent interest.
- Johan van Benthem (2008): Natural Logic: A View from the 1980s. In M. K. Chakraborty et al., editors: Logic, Navya-Nyaya and Applications: Homage to Bimal Krishna Matilal, College, London, pp. 21–42.
- Cristian S. Calude, Peter H. Hertling & Karl Svozil (1999): Embedding Quantum Universes in Classical Ones. Foundations of Physics 29, p. 349–379, 10.1023/A:1018862730956.
- John Corcoran (1972): Completeness of an Ancient Logic. J. Symb. Log. 37(4), pp. 696–702, 10.2307/2272415.
- Alex Kruckman & Lawrence S. Moss (2021): Exploring the Landscape of Relational Syllogistic Logics. The Review of Symbolic Logic 14(3), p. 728–765, 10.1017/S1755020320000386.
- Marko Malink (2013): Aristotle’s Modal Syllogistic. Harvard University Press, Cambridge, MA, 10.4159/harvard.9780674726352.
- John N. Martin (1997): Aristotle’s Natural Deduction Reconsidered. History and Philosophy of Logic 18(1), pp. 1–15, 10.1080/01445349708837269.
- Larry Moss (2011): Syllogistic Logic with Complements. In Johan van Benthem, Amitabha Gupta & Eric Pacuit, editors: Games, Norms and Reasons, Springer, pp. 179–197, 10.1007/978-94-007-0714-6_11.
- Larry Moss (2015): Natural Logic. In Chris Fox & Shalom Lappin, editors: Handbook of Contemporary Semantic Theory, 2 edition, Wiley-Blackwell Publishing, pp. 646–681, 10.1002/9781118882139.ch18.
- Anantha Padmanabha, R. Ramanujam & Yanjing Wang (2018): Bundled Fragments of First-Order Modal Logic: (Un)Decidability. In Sumit Ganguly & Paritosh K. Pandya, editors: Proceedings of FSTTCS 2018, LIPIcs 122, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, pp. 43:1–43:20, 10.4230/LIPIcs.FSTTCS.2018.43.
- Clarence Lewis Protin (2022): A Logic for Aristotle’s Modal Syllogistic. History and Philosophy of Logic 0(0), pp. 1–22, 10.1080/01445340.2022.2107382.
- Adriane Rini (2011): Aristotle’s Modal Proofs. Springer, 10.1007/978-94-007-0050-5.
- Sara L. Uckelman & Spencer Johnston (2010): A Simple Semantics for Aristotelian Apodeictic Syllogistics. In Valentin Goranko Lev Beklemishev & Valentin Shehtman, editors: Advances in Modal Logic, 8, World Scientific Publishing, pp. 454–469.
- Yanjing Wang (2017): A New Modal Framework for Epistemic Logic. In Jérôme Lang, editor: Proceedings of TARK 2017, EPTCS 251, pp. 515–534, 10.4204/EPTCS.251.38.
- Yanjing Wang (2018): Beyond Knowing That: A New Generation of Epistemic Logics, pp. 499–533. Springer International Publishing, Cham, 10.1007/978-3-319-62864-6_21.