This page is maintained by Valentin Goranko. Last update: 01/04/2020, 18.20
Lectures  Dates  Main Topics  Recommended readings  Supplementary readings 
Slides (to be posted on Athena after the lectures)  Exercises and selected solutions (to be posted on Athena)  Assignments and deadlines 

Lecture 1  26/03  Introduction to the course. Brief history and philosophical origins of logic. Logical ideas in the antiquity: Aristotle, the Stoic and Megarian schools. An overview of the spectrum of philosophical logics. The range of philosophical logics. Modes of truth, modalities and a spectrum of modal logics. Necessary and possible truths. Alethic modal logics. Possible worlds semantics: informal introduction.

R. Ballarin, Modern Origins of Modal Logic, Stanford Encyclopedia of Philosophy James Garson, Modal Logic, Stanford Encyclopedia of Philosophy. 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. For more practicing and fun with possible worlds semantics, go to this Modal Logic Playground

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 1218 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) 
Posted on Athena Introduction to the course Introduction to Modal Logics: Part I 
Posted on Athena 

Lecture 2 
30/03  Possible worlds semantics: technical introduction. Truth and validity of modal formulae. Standard translation of modal formulae to firstorder 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. Johan van Benthem, "Modal Logic for Open Minds", Chapter 2 Stefan Wölfl, Introduction to Modal Logics, Lecture notes (July 22, 2015), Sections 1, 2.12.6, 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 Logic, College Publications, 2015. (A few copies are available at the SU library), Ch. 1.3, 2.1, 2.2, 2.3

Posted on Athena: Introduction to Modal Logics: Lectures 1 and 2.

Posted on Athena 
Assignment 1 posted on Athena. 
Lecture 3  06/04  Semantic and deductive approaches to modal logics. Introduction to modal deductive systems. Axiomatic systems and semantic tableaux for modal logics. Bisimulations and bisimulation invariance of modal formulae 
On modal deductive systems: Richard Zach, Boxes and Diamonds, Open Logic Project, Chapters 3, 6. Sara Negri, Proof theory for modal logic, Philosophy Compass, vol. 6, 2011, pp. 523538. Sections 14. Melvin Fitting, Prefixed Tableaus and Nested Sequents, Annals of Pure and Applied Logic, vol. 163 (2012), pp. 291–313. Sections 13 Rajeev Goré, Tableau Methods for Modal and Temporal Logics, in: Handbook of Tableau Methods pp 297396. Sections 14.6 On bisimulations: 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) Stefan Wölfl, Introduction to Modal Logics, Lecture notes (July 22, 2015), Section 2.7. Johan van Benthem, "Modal Logic for Open Minds", Sections 3.13.4

Handbook of Modal Logic. Elsevier (2007)(available electronically from the university library), Chapters: P. Blackburn and J. van Benthem, Modal Logic: a Semantic perspective, and Melvin Fitting, Modal Proof Theory, Sections 17 (selectively). Melvin Fitting, Prefixed Tableaus and Nested Sequents, Annals of Pure and Applied Logic, vol. 163 (2012), pp. 291–313. Sections 47 Rajeev Goré, Tableau Methods for Modal and Temporal Logics, in: Handbook of Tableau Methods pp 297396. Section 4.14 Dag Prawitz, Natural Deduction: A ProofTheoretical Study, 1965. Chapter VI. (Republished by Dover Publications, 2006. Available from SU Frescatibiblioteket and Matematiska biblioteket) Stefan Wölfl, Introduction to Modal Logics, Lecture notes (July 22, 2015), Chapter 5. Valentin Goranko and Martin Otto, Model theory of Modal Logic, chapter in: Handbook of Modal Logic. Elsevier (2007) (available electronically from the university library), Section 2. 
Introduction to modal deductive systems. Axiomatic systems and semantic tableaux for modal logics. Bisimulations and bisimulation invariance of modal formulae


Lecture 4  09/04 
Reasoning about knowledge. Singleagent epistemic modal logics. Some paradoxes of knowledge and knowability. Introduction to multiagent epistemic reasoning and logics. Individual, group, distributed, and common knowledge.

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 Paul Gochet and Pascal Gribomont Rod Girle, Modal Logics and Philosophy, McGillQueen's University Press, 2nd ed., 2009, Ch.12, Epistemic logic, pp. 178199 (available from the SU library) B. Brogaard and J. Salerno, Fitch's Paradox of Knowability, Stanford Encyclopedia of Philosophy

Introduction to singleagent epistemic modal logics. Introduction to multiagent epistemic reasoning and logics. Part I.

Exercises and selected answers on singleagent epistemic logic Exercises and selected answers on multiagent epistemic logic, Part I. 

Lecture 5  16/04  Multiagent epistemic models and formal HintikkaKripke semantics for multiagent epistemic logics. Modelling, formalising and solving some epistemic puzzles and problems. Deduction in multiagent epistemic logics (briefly)

J. van Benthem, H. van Ditmarsch, J. van Eijck, J. Jaspars, Logic in Action, Ch. 5. Knowledge and Information Flow, Open Course Project, University of Amsterdam 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 multiagent epistemic reasoning and logics (complete)
Introduction to dynamic epistemic logic, Part I. 
Exercises and selected answers on multiagent epistemic logic (full) 
Submission of Assignment 1. Deadline: 16.00 on April 17.

Lecture 6  23/04  Introduction to dynamic epistemic logic. Epistemic actions and epistemic model updates. Reasoning about beliefs and doxastic modal logics.

On dynamic epistemic logics: Eric Pacuit. Dynamic Epistemic Logic II: Logics of Information Change. Philosophy Compass, 8:9, pgs. 815  833, 2013. On doxastic 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. 120 in: Belief Revision, P. Gärdenfors (ed), Cambridge University Press, 1992

On dynamic epistemic logics: J. Gerbrandy , The Surprise Examination in Dynamic Epistemic Logic, Synthese, Vol. 155, No. 1 (Mar., 2007), pp. 2133 On belief revision and doxastic logics: SvenOve Hansson, Logic of Belief Revision, Stanford Encyclopedia of Philosophy

Introduction to dynamic epistemic logic. Introduction to doxastic modal logics

Exercises and selected answers on:  dynamic epistemic logic.  doxastic logics

Assignment 2 to be posted

Lecture 7  27/04 
Reasoning about time.Tense and modality. Historical necessity and Diodorus' Master Argument. Variety of temporal models. Prior's basic temporal logic and some extensions. Linear time temporal logics. The linear time temporal logic LTL.

Valentin Goranko and Antony Galton, Temporal Logic, Stanford Encyclopedia of Philosophy, Sections 14.

Peter Øhrstrøm and Per Hasle, Future Contingents, Stanford Encyclopedia of Philosophy B. Jack Copeland, Arthur Prior, Stanford Encyclopedia of Philosophy J. van Benthem, Tense logic and time. Notre Dame J. Formal Logic 25 (1984), no. 1, 116. 
Introduction to temporal logics Linear time temporal logics. The logic LTL. 
Exercises and selected answers on temporal logic  part I 

Lecture 8  04/05  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 Antony Galton, 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 M ̈uller, Time and Determinism, J Philos Logic (2015) 44:729–740.

Exercises and selected answers on temporal logic  part II: branching time logics 

Lecture 9  07/05  Transition semantics for branching time (presented by Antje Rumberg) Models and logics of agency. `Seeing to it That' (STIT) theory and variations.

Nuel Belnap & Michael Perloff, Seeing to it that: a canonical form for agentives, Theoria 54 (3):175199 (1988). A corrected version republished in: Knowledge Representation and Defeasible Reasoning, (Loui Kyberg, Jr. and Carlson (eds.)), Kluwer, Dordrecht, 1990, pp. 167–90. (available electronically from the SU library)

Nuel Belnap, Michael Perloff and Ming Xu, Facing the Future: Agents and Choices in Our Indeterminist World. Oxford University Press, 2001. (available electronically from the SU library) Brian Chellass, Time and Modality in the Logic of Agency, Studia Logica, vol 51. 1992, pp. 485517 Mark A. Brown: On the logic of ability. J. Phil. Logic 17(1), 1988, pp. 126 Jan M. Broersen, Andreas Herzig: Using STIT Theory to Talk About Strategies. in: Models of Strategic Reasoning: Logics, Games and Communities, J. van Benthem, S. Ghosh, R. Verbrugge (eds.), Springer, LNCS/FoLLI series, vol. 8972, 2015, pp. 137173. Sections 1, 2, 3.1 

Exercises and selected answers on STIT 
Submission of Assignment 2

Lecture 10 
11/05  Karl Nygren: Normative reasoning and deontic logics.

Paul McNamara, Deontic Logic, Stanford Encyclopedia of Philosophy Pablo Navarro and Jorge Rodríguez, Deontic Logic and Legal Systems, Cambridge University Press, 2014, Chapters 1 (1.31.5), 2 (available electronically from the SU library) John Horty, Agency and Deontic Logic, Oxford UP, 2001, Chapters 3, 4. (available electronically from the SU library)

G. H. von Wright, On the Logic of Norms and Actions, in: New Studies in Deontic Logic Norms, Actions, and the Foundations of Ethics, R. Hilpinen (Ed.), Synthese, 1981 (available electronically from the SU library) D. Føllesdal and R. Hilpinen. “Deontic Logic: An Introduction.” In: Deontic Logic: Introductory And Systematic Readings, R. Hilpinen (Ed), Reidel, Dordrecht, 1971, pp 1–35. (available electronically from the SU library) Lennart Åqvist, “Deontic Logic.” In Gabbay and Guenthner, 2nd ed. vol. 8(2002), pp147–264. (First edition 1984) (also available electronically from the SU library)



Assignment 3 to be posted

Lecture 11  18/05  Introduction to firstorder modal logics (FOML): Interactions between modality and quantification. Formal semantics of FOML. Possibilist and actualist semantics. Models and logics with constant and variable domains. Barcan formulae. 
w. Quine, Three Grades of Modal Involvement, in: the Proceedings of the Xlth Intern. Congress of Philosophy, Brussels, 1953, Volume 14 (Available on Athena) R. Ballarin, Quine on intensional entities: Modality and quantification, truth and satisfaction, Journal of Applied Logic 10 (2012) 238–249. (Available on Athena) Melvin Fitting and Richard L. Mendelsohn, Firstorder modal logic, Kluwer, Synthese Library, 1998, Chapter 4, 612, (available electronically from the SU library) 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. (available electronically from the SU library) George Hughes and Max Cresswell, A new introduction to modal logic, Routledge, 1996. Ch 13, pp 235255; Ch 15, pp 274287. (available electronically from the SU library) 
James Garson, Modal Logic, Stanford Encyclopedia of Philosophy. Gary Hardegree, Introduction to Modal Logic, Ch.6,8,9,10 Ted Sider, Logic for Philosophy, OUP, 2010, (available from the SU library), Chapter 9. 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) Francesco Belardinelli, Counterpart Semantics for Quantified Modal Logic, 2007 Torben Braüner and Silvio Ghilardi, Firstorder modal logic, Chapter 9 in: Handbook of Modal Logic, Elsevier, 2007, pp. 549620 (available electronically from the SU library) 


Lecture 12  20/05  Firstorder temporal and epistemic logics Introduction to intuitionistic logic.

Melvin Fitting and Richard L. Mendelsohn, Firstorder modal logic, Kluwer, Synthese Library, 1998, Chapter 4, 612, (available electronically from the SU library) Joan Moschovakis, Intuitionistic Logic, Stanford Encyclopedia of Philosophy 
Erik Palmgren, Semantics of intuitionistic propositional logic, Lecture Notes, 2009 Yaroslav Shramko, Heinrich Wansing: Truth values, Stanford Encyclopedia of Philosophy 

Lecture 13  25/05  Introduction to manyvalued logics. Introduction to logics of conditionals and to relevance logics. Conclusion of the course 
Siegfried Gottwald, ManyValued Logic, Stanford Encyclopedia of Philosophy H. ArloCosta and Paul Egré, The Logic of Conditionals, Stanford Encyclopedia of Philosophy Edwin Mares, Relevance Logic, Stanford Encyclopedia of Philosophy 
Paul Egre and Mikael Cozic, Introduction to the Logic of Conditionals, ESSLLI 2008 Course material 
Submission of Assignment 3 

Lecture 14  01/06  Spare slot Return of assignment 3. Final disucssion. 





Lecture notes, slides and other reading material will be provided or linked to this page on an ongoing basis.
General on philosophical logic
On generic modal logics:
On epistemic logics, dynamic epistemic logics, logics of belief and belief revision:
On temporal logics:
On logics for ability, actions, agency and STIT:
On deontic logics:
On firstorder modal ogics:
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.
If you have any queries on the information above, talk to me or send me an email.