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Philosophical Logic I

Last update: 18/05/2022, 13.00
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Lecturer: Valentin Goranko

SI meetings leaders: Alexander Lind, Leo Marklund, Mikael Eriksson

Departmental course page

Schedule

Detailed course plan:

(Preliminary version. Updates will be made frequently.)

Lecture 1

Date 24/03

Main Topics

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.

Recommended readings

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.

 

Supplementary readings

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)

Online tools:

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

Slides posted on Athena

Introduction to the course

Introduction to Modal Logics: Part I

Exercises and selected solutions posted on Athena

Assignments and deadlines

Lecture 2

Date 13/04

Main Topics

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.

Recommended readings

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.

Supplementary readings

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

Gary Hardegree, Introduction to Modal Logic, Ch.5

Saul A. Kripke, Semantical Analysis of Modal Logic I. Normal Modal Propositional Calculi, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96 (1963)

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

Slides posted on Athena:

Introduction to Modal Logics. Part II.

Exercises and selected solutions posted on Athena

Assignments and deadlines

Lecture 3

Date 14/04

Main Topics

Semantic and deductive approaches to modal logics.

Introduction to modal deductive systems.

Axiomatic systems and semantic tableaux for modal logics.

Recommended readings

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

Supplementary readings

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 1-7 (selectively).

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.

Online tools:

MOLTAP — A Modal Logic Tableau Prover

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

Slides posted on Athena:

Introduction to modal deductive systems.

Axiomatic systems and semantic tableaux for modal logics.

Exercises and selected solutions (posted on Athena)

Assignments and deadlines

Assignment 1 to be posted.

Lecture 4

Date 25/04

Main Topics

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.

Recommended readings

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)

R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning About Knowledge, MIT Press, 1995. Chapters 1,2; pages 1-45

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

H. van Ditmarsch, J.Y. Halpern, W. van der Hoek, B. Kooi "An Introduction to Logics of Knowledge and Belief ". Chapter 1 in: Handbook of Epistemic Logic, College Publications, 2015, pp. 1-51.

Roy Sorensen, Epistemic Paradoxes, Stanford Encyclopedia of Philosophy

Supplementary readings

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

Slides (posted on Athena)

Introduction to single-agent epistemic modal logics.

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

Exercises and selected solutions (posted on Athena)

Exercises and selected answers on single-agent epistemic logic

Assignments and deadlines

Lecture 5

Date 28/04

Main Topics

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)

Recommended readings

On multi-agent epistemic logics

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

Hans van Ditmarsch Joseph Y. Halpern Wiebe van der Hoek Barteld Kooi, An Introduction to Logics of Knowledge and Belief, Ch. 1 in Handbook of Epistemic logic, College Publications, 2015. pp. 1-50

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

Supplementary readings

On multi-agent epistemic logics

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

Nick Bezhanishvili and Wiebe van der Hoek, Structures for Epistemic Logic, in: Johan van Benthem on Logic and Information Dynamics, Springer, 2014, pp 339-381.

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

Online tools:

MOLTAP — A Modal Logic Tableau Prover (also with tableaux for multi-agent epistemic logic, with individual knowledge and incomplete version of common knowledge)

Slides (posted on Athena)

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

Exercises and selected solutions (posted on Athena)

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

Assignments and deadlines

Submission of Assignment 1: April 29.

Assignment 2 to be posted

Lecture 6

Date 4/05

Main Topics

Reasoning about beliefs and doxastic modal logics.

Recommended readings

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

A. Baltag, H. P. van Ditmarsch and L.S. Moss. "Epistemic logic and information update". Handbook of Philosophy of Information, in the series Handbook of Philosophy of Science, vol. 8, pp. 361-455, Elsevier, 2008.

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

Supplementary readings

Joseph Y. Halpern, Should knowledge entail belief? Journal of Philosophical Logic volume 25, pages 483–494(1996)

Robert Stalnaker, On Logics of Knowledge and Belief, Philosophical Studies, volume 128, pages 169–199(2006)

Johan van Benthem, Dynamic logic for belief revision, J. of Applied Non-Classical Logics, vol.14, No. 2, 2004

H. van Ditmarcsh, W. van der Hoek and B. Kooi, Dynamic Epistemic Logic, Springer, Synthese Library series, 2008, Ch. 2.4 and 3

Johan van Benthem and Sonja Smets, Dynamic Logics of Belief Change, Ch. 1 in Handbook of Epistemic logic, College Publications, 2015. pp. 299–368

Alexandru Baltag and Sonja Smets, Conditional Doxastic Models: A Qualitative Approach to Dynamic Belief Revision, Electronic Notes in Theoretical Computer Science 165 (2006) 5–21

Hannes Leitgeb and Krister Segerberg, Dynamic Doxastic Logic: Why, How, and Where To?, Synthese Vol. 155, No. 2, (Mar., 2007), pp. 167-190

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

Online tools:

Hintikka's world: an animated website for multi-agent epistemic logic. Lots of examples and exercises on epistemic puzzles.

Slides (posted on Athena after the lectures)

Introduction to doxastic modal logics

Exercises and selected solutions (posted on Athena)

Exercises and selected answers on doxastic logics

Assignments and deadlines

Lecture 7

Date 6/05

Main Topics

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.

Recommended readings

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

Thomas Mueller: Tense or Temporal Logic, Chapter 12 in: The Continuum Companion to Philosophical Logic, R. Pettigrew and L. Horsten (eds.), 2011

John Burgess: Philosophical Logic, Princeton University Press, 2009. (available electronically from the SU library) Ch.2: Temporal Logic (2.1-2.6)

P. Øhrstrøm and Per Hasle: Temporal Logic: From Ancient Ideas to Artificial Intelligence. Kluwer, 1995. Reprinted by Springer. (available electronically from the SU library) Chapters 1.2, 2.5, 2.8

Supplementary readings

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

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

Yde Venema, Temporal Logic, chapter in: Lou Goble (ed), Blackwell Guide on Philosophical Logic, Blackwell Publishers, 2001

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)

Slides (posted on Athena)

Introduction to temporal logics

Exercises and selected solutions (posted on Athena)

Exercises and selected answers on temporal logics. Part I

Assignments and deadlines

Lecture 8

Date 11/05

Main Topics

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

Recommended readings

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

Supplementary readings

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

Slides (posted on Athena)

Linear time temporal logics. The logic LTL.

Exercises and selected solutions (posted on Athena)

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

Assignments and deadlines

Lecture 9

Date 13/05

Main Topics

Derivation of Diodorus' Master Argument. Possible solutions.

Models of branching time and historical necessity.

The Ockhamist and the Peircean branching time temporal logics.

Recommended readings

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.

P. Øhrstrøm and Per Hasle, Temporal Logic: From Ancient Ideas to Artificial Intelligence. Kluwer, 1995. Reprinted by Springer. Chapters 2.6, 2.8, 2.10

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;

Supplementary readings

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)

P. Øhrstrøm, Towards a Common Language for the Discussion of Time Based on Prior’s Tense Logic, in: Time and Time Perception, Springer LNAI 6789, pp. 46–57, 2011.

Peter Øhrstrøm: A critical discussion of Prior’s philosophical and tense-logical analysis of the ideas of indeterminism and human freedom, Synthese, 2016

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

Slides (posted on Athena)

Branching time temporal logics.

Exercises and selected solutions (posted on Athena)

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

Assignments and deadlines

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

Lecture 10

Date 16/05

Main Topics

Introduction to intuitionistic logic.

Recommended readings

Joan Moschovakis, Intuitionistic Logic, Stanford Encyclopedia of Philosophy

Dirk van Dalen, Intuitionistic Logic, in: The Blackwell Guide to Philosophical Logic, L. Gobble (ed), Blackwell, Oxford. 2001, 224–257.

Graham Priest, An Introduction to Non-Classical Logic: From If to Is, Cambridge University Press, 2012 (2nd edition). (Available electronically from the SU library) Chapter 6.

Supplementary readings

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

Slides (posted on Athena)

Introduction to intuitionistic logic.

Exercises and selected solutions (posted on Athena)

Exercises and selected answers on intuitionistic logic

Assignments and deadlines

Lecture 11

Date 19/05

Main Topics

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

Recommended readings

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

Nicholas J.J. Smith, Many-valued logics, in: Routledge Companion to the Philosophy of Language, 2010, Article 2.6.

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

Graham Priest, An Introduction to Non-Classical Logic: From If to Is, Cambridge University Press, 2012 (2nd edition). (Available electronically from the SU library) Chapters 7-10.

Supplementary readings

Alasdair Urquhart, Basic Many-Valued Logic, Handbook of Philosophical Logic, vol 2 (2nd ed.), 2001, pp 249-295

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

Graham Priest, An Introduction to Non-Classical Logic: From If to Is, Cambridge University Press, 2012 (2nd edition). (Available electronically from the SU library) Chapters 11, 11a.

Slides (posted on Athena)

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

Exercises and selected solutions (posted on Athena)

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

Assignments and deadlines

Submission of Assignment 3: 30/05

Lecture 12

Date 02/06

Main Topics

Capita selecta.

Feedback on assignment 3 and final discussion.

Conclusion of the course.

General course details

Schedule time-table

Link to time-table

Departmental course page with plan and course description

Link to departamental course page

Lecture notes, handouts, and other reading material

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

Exercises

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.

Assignments and final grade

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.

Additional readings and exercises

Readings

General on philosophical logic

On generic modal logics

On epistemic logics, dynamic epistemic logics, logics of belief and belief revision

On temporal logics

Queries

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

Mail to V.Goranko