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Last update: 18/05/2022, 13.00

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** Date 24/03 **

Introduction to the course.

The range of philosophical logics: an overview.

Modes of truth. The variety of modalities and modal logics.

Necessary and possible truths. Alethic modal logics.

Possible worlds semantics: introduction. Truth of modal formulae in Kripke models.

R. Ballarin, *Modern Origins of Modal Logic,* Stanford Encyclopedia of Philosophy

James Garson, *Modal Logic,* Stanford Encyclopedia of Philosophy, Sections 1-6

Richard Zach, *Boxes and Diamonds*, Open Logic Project, Chapter 1

Eric Pacuit, *Lecture notes on modal Logic*, Sect.1, 2

Johan van Benthem, "*Modal Logic for Open Minds*", Chapters 1. 2

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): subsection 1.1.

Gary Hardegree, *Introduction to Modal Logic,* Ch.1,3,4

Ed Zalta, *Basic Concepts of Modal Logic*, Lecture notes, CSLI, Stanford University, Chapters 1, 2, 3(§1-§3)

Introductions to Part III and chapters 12-18 of the 02/02/2010 draft of the book "Modal Logic for Open Minds" by Johan van Benthem here).

P. Blackburn and J. van Benthem, *Modal Logic: a Semantic perspective*, Sections 1,2. Chapter in *Handbook of Modal Logic.* Elsevier (2007) (available electronically from the university library)

For more practicing and fun with possible worlds semantics, go to this Modal Logic Playground

Introduction to the course

Introduction to Modal Logics: Part I

** Date 13/04 **

Possible worlds semantics: notions of validity and logical consequence of modal formulae.

Standard translation of modal formulae to first-order logic.

Some important modal principles and systems of modal logic.

Frame validity of modal formulae. Frame definability and correspondence.

Richard Zach, * Boxes and Diamonds,* Open Logic Project, Chapter 2.

Eric Pacuit, *Lecture notes on modal Logic*, Sections 3,4

James Garson, *Modal Logic*, Stanford Encyclopedia of Philosophy, Sections 7-8.

Johan van Benthem, "** Modal Logic for Open Minds**", Chapter 2

Stefan Wölfl, *Introduction to Modal Logics*, Lecture notes (July 22, 2015), Sections 1, 2.1-2.6, 3.1,3.2, 3.6.

Ed Zalta, *Basic Concepts of Modal Logic*, Lecture notes, CSLI, Stanford University, Ch. 3,4,5.

Gary Hardegree, *Introduction to Modal Logic*, Ch.5

Lloyd Humberstone, ** Philosophical Applications of Modal Logi**c, College Publications, 2015. (A few copies are available at the SU library), Ch. 1.3, 2.1, 2.2, 2.3

Introduction to Modal Logics. Part II.

** **

** Date 14/04 **

Semantic and deductive approaches to modal logics.

Introduction to modal deductive systems.

Axiomatic systems and semantic tableaux for modal logics.

Richard Zach, * Boxes and Diamonds*, Open Logic Project, Chapters 3, 6.

Sara Negri, *Proof theory for modal logic,* Philosophy Compass, vol. 6, 2011, pp. 523-538. Sections 1-4.

Melvin Fitting, *Prefixed Tableaus and Nested Sequents*, Annals of Pure and Applied Logic, vol. 163 (2012), pp. 291–313. Sections 1-3

Rajeev Goré, *Tableau Methods for Modal and Temporal Logics*, in: * Handbook of Tableau Methods,* pp 297-396. Sections 1-4.6

* Handbook of Modal Logic*. Elsevier (2007)(available electronically from the university library), Chapters: P. Blackburn and J. van Benthem,

Melvin Fitting, *Prefixed Tableaus and Nested Sequents,* Annals of Pure and Applied Logic, vol. 163 (2012), pp. 291–313. Sections 4-7

Rajeev Goré, *Tableau Methods for Modal and Temporal Logics*, in: * Handbook of Tableau Methods* pp 297-396. Section 4.14

Dag Prawitz, Natural Deduction: A Proof-Theoretical Study, 1965. Chapter VI. (Re-published by Dover Publications, 2006. Available from SU Frescatibiblioteket and Matematiska biblioteket)

Stefan Wölfl, *Introduction to Modal Logics*, Lecture notes (July 22, 2015), Chapter 5.

MOLTAP — A Modal Logic Tableau Prover

Tableaunoir - A Modal Logic Tableau Prover , Video presentation of Tableaunoir

Introduction to modal deductive systems.

Axiomatic systems and semantic tableaux for modal logics.

** Assignment 1 to be posted. **

** Date 25/04 **

Reasoning about knowledge. Single-agent epistemic modal logics. Alethic-epistemic logics.

Some paradoxes of knowledge and knowability.

Introduction to multi-agent epistemic reasoning and logics. Individual, group, distributed, and common knowledge.

Jaakko Hintikka, Knowledge and belief: an introduction to the logic of the two notions, Cornell University Press, 1962 (in the SU library and on Athena)

Chapter 12 of the book "** Modal Logic for Open Minds**" by Johan van Benthem (available from the SU library)

*Chapter on Epistemic Logic* from the book "** Dynamic Epistemic Logic**" by H. van Ditmarcsh, W. van der Hoek and B. Kooi, Ch 2.1, 2.2

Roy Sorensen, Epistemic Paradoxes, Stanford Encyclopedia of Philosophy

V. Hendricks and J. Symons, *Epistemic Logic*, Stanford Encyclopedia of Philosophy, Section 1

Rod Girle, *Modal Logics and Philosophy*, McGill-Queen's University Press, 2nd ed., 2009, Ch.12, Epistemic logic, pp. 178-199 (available from the SU library)

B. Brogaard and J. Salerno, *Fitch's Paradox of Knowability,* Stanford Encyclopedia of Philosophy

Introduction to single-agent epistemic modal logics.

Introduction to multi-agent epistemic reasoning and logics. Part I.

Exercises and selected answers on single-agent epistemic logic

** Date 28/04 **

Multi-agent epistemic models and formal Hintikka-Kripke semantics for multi-agent epistemic logics.

Brief introduction to dynamic epistemic logic: public announcements and model updates.

Modelling, formalising and solving some epistemic puzzles and problems.

On deduction in multi-agent epistemic logics (briefly)

J. van Benthem, H. van Ditmarsch, J. van Eijck, J. Jaspars, * Logic in Action*,

Chapter on Epistemic Logic from the book "Dynamic Epistemic Logic" by H. van Ditmarcsh, W. van der Hoek and B. Kooi, Ch 2.3

Eric Pacuit. *Dynamic Epistemic Logic I: Modelling Knowledge and Belief.* Philosophy Compass, 8:9, pgs. 798 - 814, 2013. Sections 1,2,4.

V. Hendricks and J. Symons, *Epistemic Logic*, Stanford Encyclopedia of Philosophy

Chapter on *Epistemic logic: knowledge and belief* from the book * Modalities and Multimodalities* by W. Carnielli and C. Pizzi

Introduction to multi-agent epistemic reasoning and logics. Part II.

Exercises and selected answers on multi-agent epistemic logic. Part II.

** Submission of Assignment 1: April 29. **

** Assignment 2 to be posted**

** Date 4/05 **

Reasoning about beliefs and doxastic modal logics.

Eric Pacuit. *Dynamic Epistemic Logic I: Logics of Knowledge and Belief.* Philosophy Compass, 8:9, pgs. 798 - 814, 2013. Section 3

Peter Gärdenfors, Belief Revision: An Introduction, pp. 1-20 in: Belief Revision, P. Gärdenfors (ed), Cambridge University Press, 1992

Sven-Ove Hansson, Logic of Belief Revision, Stanford Encyclopedia of Philosophy

Eric Pacuit. *Ten Puzzles and Paradoxes about Knowledge and Belief.* Short course given at ESSLLI 2013.

Thomas Ågotnes and Yì N. Wáng, Group belief, 2020

Introduction to doxastic modal logics

Exercises and selected answers on doxastic logics

** Date 6/05 **

Introduction to temporal logics: Reasoning about time. Tense and modality. Variety of temporal models.

Historical necessity and Diodorus' Master Argument.

Prior's basic temporal logic and some extensions.

Valentin Goranko and Antje Rumberg, Temporal Logic, Stanford Encyclopedia of Philosophy. Sections 1-3.

B. Jack Copeland, Arthur Prior, Stanford Encyclopedia of Philosophy

Peter Øhrstrøm and Per Hasle, Future Contingents, Stanford Encyclopedia of Philosophy

J. van Benthem, Tense logic and time. Notre Dame J. Formal Logic 25 (1984), no. 1, 1--16.

Rob Goldblatt, Logics of Time and Computations, CSLI pubblications, 2nd revised and expanded edition, 1992 Chapter 6 (electronic copy available on Athena)

Introduction to temporal logics

Exercises and selected answers on temporal logics. Part I

** Date 11/05 **

Linear time temporal logics. The linear time temporal logic LTL.

Valentin Goranko and Antje Rumberg, Temporal Logic, Stanford Encyclopedia of Philosophy, Section 4

Rob Goldblatt, Logics of Time and Computations, CSLI pubblications, 2nd revised and expanded edition, 1992 Chapter 8 (electronic copy available on Athena)

Linear time temporal logics. The logic LTL.

Exercises and selected answers on temporal logics. Part II: linear time logics

** Date 13/05 **

Derivation of Diodorus' Master Argument. Possible solutions.

Models of branching time and historical necessity.

The Ockhamist and the Peircean branching time temporal logics.

Valentin Goranko and Antje Rumberg, Temporal Logic, Stanford Encyclopedia of Philosophy, Section 5

Nicholas Denyer: Diodorus Cronus: Modality, The Master Argument and Formalisation. in: Humana.Mente, vol. 8, 2009 (Special issue on "Models of Time")

Thomas Ploug and Peter Øhrstrøm: Branching time, indeterminism and tense logic Unveiling the Prior–Kripke letters, Synthese (2012) 188: 367–379.

Two articles in Journal of Philosophical Studies, vol. 8, 2009 (Special issue on "Models of Time"):

-- Alberto Zanardo, Modalities in Temporal Logic;

-- Peter Øhrstrøm, In Defence of the Thin Red Line: A Case for Ockhamism;

Jorge Luis Borges, The Garden of Forking Paths, 1941

A.N. Prior. *Time and Determinism*, and *The Search for the Diodorean Modal System,* in: * Past, Present and Future. Oxford University Press, 1967* (available electronically from the SU library)

Thomas Müller, Time and Determinism, J Philos Logic (2015) 44:729–740.

Branching time temporal logics.

Exercises and selected answers on temporal logic. Part III: branching time logics

** Submission of Assignment 2: 16/05. Assignment 3 to be posted. **

** Date 16/05 **

Introduction to intuitionistic logic.

Joan Moschovakis, Intuitionistic Logic, Stanford Encyclopedia of Philosophy

L.E.J. Brouwer, Intuitionism and formalism, Bull. Amer. Math. Soc. Volume 20, 2 (1913), 81-96.

Rosalie Iemhoff, Intuitionism in the Philosophy of Mathematics, Stanford Encyclopedia of Philosophy

Mark van Atten, The Development of Intuitionistic Logic, Stanford Encyclopedia of Philosophy

Erik Palmgren, Semantics of intuitionistic propositional logic, Lecture Notes, 2009

Introduction to intuitionistic logic.

Exercises and selected answers on intuitionistic logic

** Date 19/05 **

Introduction to many-valued logics, relevance, and first-degree entailment.

Siegfried Gottwald, Many-Valued Logic, Stanford Encyclopedia of Philosophy

Melvin Fitting, First Degree Entailment, Lecture notes, 2018.

Yaroslav Shramko, Heinrich Wansing: Truth values, Stanford Encyclopedia of Philosophy

Introduction to many-valued logics, relevance, and first-degree entailment.

Exercises and selected answers on many-valued logics, relevance, and first-degree entailment.

** Submission of Assignment 3: 30/05 **

Date 02/06

Capita selecta.

Feedback on assignment 3 and final discussion.

Conclusion of the course.

Link to departamental course page

Lecture notes, slides and other reading material will be provided or linked to this page on an ongoing basis.

List of exercises will be provided on a weekly basis, usually taken from the lecture notes and handouts. Students are advised to do as many exercises on each topic as they need to master it. Solutions or hints to some selected exercises will be provided and will be discussed in the discussion time before and during the lectures.

There will be **3 mandatory written assignments** during the course, each consisting of a set of exercises. The assignments will be provided about 2 weeks before the submission deadline. Students must do these exercises **individually** and prepare written reports with their solutions.

The assignments will be checked and corrected by the lecturer and the teaching assistant, then returned to the students for feedback, and then returned back to the lecturer. The average of the assignments grades will form the final grade.

- Ed Zalta (ed.), Stanford Encyclopaedia of Philosophy
- Lou Goble, The Blackwell Guide to Philosophical Logic, Wiley, 2001. (available from the SU library)
- A Companion to Philosophical Logic, Dale Jacquette (Ed.), 2006, Blackwell Publishing (available electronically from the SU library)
- John Burgess, Philosophical Logic, Princeton University Press, 2009. (available electronically from the SU library)
- Rod Girle, Modal Logics and Philosophy, McGill-Queen's University Press, 2nd ed., 2009 (available electronically from the SU library)
- Lloyd Humberstone, Philosophical Applications of Modal Logic, College Publications, 2016.
- Ted Sider, Logic for Philosophy, OUP, 2010.

- Patrick Blackburn and Johan van Benthem, Modal Logic: a Semantic perspective, in: Handbook of Modal Logic, edited by P. Blackburn, J. van Benthem and F. Wolter, Elsevier, 2007.
- Johan van Benthem, Modal Logic for Open Minds, CSLI publ., 2010. (available from the SU library)

- R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning About Knowledge, MIT Press, Revised edition 2003. Chapters 1-3 avaliable here.
- Joseph Y. Halpern, Reasoning about knowledge: a survey. In: Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 4, D. Gabbay, C. J. Hogger, and J. A. Robinson, eds., Oxford University Press, 1995, pp. 1-34.
- Vincent Hendricks and John Symons, Epistemic Logic, Stanford Encyclopedia of Philosophy.
- Joseph Y. Halpern, Dov Samet, Ella Segev. DEFINING KNOWLEDGE IN TERMS OF BELIEF: THE MODAL LOGIC PERSPECTIVE. THE REVIEW OF SYMBOLIC LOGIC, Vol. 2, Nr. 3, 2009
- Sten Lindström & Krister Segerberg, Modal Logic and Philosophy, chapter in: P. Blackburn & J. van Benthem (eds.), Handbook of Modal Logic. Elsevier (2007), Section 2 (The modal logic of belief change)
- A. Baltag, L.S. Moss, S. Solecki. "The Logic of Public Announcements, Common Knowledge and Private Suspicions". Proceedings of TARK'98 (Seventh Conference on Theoretical Aspects of Rationality and Knowledge), 43-56. 1998.
- Johan van Benthem, Jan van Eijck, and Barteld Kooi, Logics of Communication and Change. Information and Computation, Volume 204, Issue 11, 2006, Pages 1620–1662. Also available here.
- Edward T. Dean, A Brief Introduction to Belief Revision, Lecture notes, 2005.

- A.N. Prior, Time and Modality. Oxford University Press, 1957.
- A.N. Prior, Past, Present and Future. Oxford University Press, 1967.
- A.N. Prior, Papers on Time and Tense. Oxford University Press, 1968.
- P. Øhrstrøm and Per Hasle, Temporal Logic: From Ancient Ideas to Artificial Intelligence. Kluwer, 1995. Reprinted by Springer.
- M. Steedman. Temporality. In J. van Benthem and A. ter Meulen, editors, Handbook of Logic and Language, pages 895–938. Elsevier Sci- entific Publishers, Amsterdam, 1997.
- J. van Benthem, The logic of time: a model-theoretic investigation into the varieties of temporal ontology and temporal discourse, Reidel, 1983. Reprinted by Springer.

If you have any queries on the information above, talk to me or send me an email.

Mail to V.Goranko