Last update: August 4, 2023, 17.00 CEST
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Date 31/07/2023
Introduction to the course. Brief history and philosophical origins.
Technical introduction to first-order modal logics (FOML): languages, frames, and models.
Varying, increasing, decreasing, and constant domains. Formal semantics. Actualist and possibilist semantics.
Existence predicate. Reductions between actualist and possibilist semantics.
Melvin Fitting, First order alethic modal logic, A Companion to Philosophical Logic, Blackwell, 2002, pp. 410--421
Melvin Fitting and Richard L. Mendelsohn, First-order modal logic, Kluwer, Synthese Library, 1998, Chapters 4, 6.
Torben Braüner and Silvio Ghilardi, First-order modal logic, Chapter 9 in: P. Blackburn & J. van Benthem (eds.), Handbook of Modal Logic. Elsevier (2007), pp. 550-564
Sten Lindström & Krister Segerberg, Modal Logic and Philosophy, chapter 21 in: P. Blackburn & J. van Benthem (eds.), Handbook of Modal Logic. Elsevier (2007), Section 1: Alletic modal logic.
Date 01/08/2023
Axiomatic systems for first-order modal logics. Some completeness results.
George Hughes and Max Cresswell, A new introduction to modal logic, Routledge, 1996. Ch 14, Ch 15.
Date 02/08/2023
Introduction to first-order temporal logics (FOTL).
Philosophical problems of the interaction of quantification with modality. Equality, existence, necessitation, quantification de dicto and de re, definite descriptions, rigid designators.
W. Quine, Three Grades of Modal Involvement, in: the Proceedings of the Xlth Intern. Congress of Philosophy, Brussels, 1953, Volume 14
Melvin Fitting, First order alethic modal logic, A Companion to Philosophical Logic, Blackwell, 2002, pp. 410--421
Melvin Fitting and Richard L. Mendelsohn, First-order modal logic, Kluwer, Synthese Library, 1998, Chapters 7,8, 11, 12.
Sten Lindström & Krister Segerberg, Modal Logic and Philosophy, chapter in: P. Blackburn & J. van Benthem (eds.), Handbook of Modal Logic. Elsevier (2007), Section 1: Alletic modal logic.
Melvin Fitting, Barcan Both Ways, Journal of Applied Non-Classical Logics 9(2-3), 1999
Introduction to first-order temporal logics
Philosophical issues and problems in FOML and FOTL
Date 03/08/2023
Undecidability, non-axiomatizabilty, and complexity of the decision problems for some important systems of FOML and FOTL.
Some decidable systems and fragments of FOML and FOTL.
Roman Kontchakov, Agi Kurucz and Michael Zakharyaschev. Undecidability of first-order intuitionistic and modal logics with two variables. Bulletin of Symbolic Logic, 11(3):428-438, 2005.
Frank Wolter and Michael Zakharyaschev. Decidable Fragments of First-Order Modal Logics. Journal of Symbolic Logic, 66(3):1415-1438, 2001.
Mikhail Rybakov and Dmitry Shkatov. Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter. Studia Logica, 107(4):695–717, 2019.
Computational properties of rst-order modal and temporal logics
Date 04/08/2023
Variety of other formal semantics of FOML: counterpart semantics, metaframe semantics, generalised semantics.
Predicate abstractions for FOML.
Conclusion of the course.
Melvin Fitting and Richard L. Mendelsohn, First-order modal logic, Kluwer, Synthese Library, 1998, Chapters 9, 10.
Francesco Belardinelli. Counterpart Semantics for Quantified Modal Logic, 2007.
Marcus Kracht, Oliver Kutz. Logically Possible Worlds and Counterpart Semantics for Modal Logic, Philosophy of Logic Handbook, 2007, Pages 943-995.
Melvin Fitting, Intensional Logic, Stanford Encyclopedia of Philosophy.
Torben Braüner and Silvio Ghilardi, First-order modal logic, Chapter 9 in: P. Blackburn & J. van Benthem (eds.), Handbook of Modal Logic. Elsevier (2007), pp. 607-613.
Giovanna Corsi. Counterpart Semantics. A Foundational study on Quantified Modal Logics, 2002.
M. Cresswell, Rudolf Carnap: Modal Logic, Internet Encyclopedia of Philosophy
R. Carnap, Modalities and Quantification, J. of Symb. Logic, Vol. 11, Nr 2, 1946. (Available on Athena)
James Garson, Modal Logic, Stanford Encyclopedia of Philosophy.
Gary Hardegree, Introduction to Modal Logic, Ch.6,8,9,10
Melvin Fitting, Barcan Both Ways, Journal of Applied Non-Classical Logics, Vol. 9, Issue 2-3, 1999, pp. 329-344.
Ted Sider, Logic for Philosophy, OUP, 2010, (available from the SU library), Chapter 9.
Ed Zalta, Basic Concepts of Modal Logic, Lecture notes, CSLI, Stanford University, Chapter 6
Francesco Belardinelli, Counterpart Semantics for Quantified Modal Logic, 2007
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