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24.244

Modal Logic

3-0-9 units. HASS-H · Undergraduate

Sentential and quantified modal logic, with emphasis on the model theory ("possible worlds semantics"). Soundness, completeness, and characterization results for alternative systems. Tense and dynamic logics, epistemic logics, as well as logics of necessity and possibility. Applications in philosophy, theoretical computer science, and linguistics. Enrollment may be limited.

Spring 2015

Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligation and permission, the known and the not-ruled-out. This a first course in the area. A solid background in first-order logic is essential. Topics to be covered include (some or all of) the main systems of propositional modal logic, Kripkean "possible world" semantics, strict implication, contingent identity, intensional objects, counterpart theory, the logic of actuality, and deontic and / or epistemic logic. The emphasis will be more on technical methods and results than philosophical applications.

Readings

  • Readings are from Hughes, and Cresswell. A New Introduction to Modal Logic . Routledge, 1996. ISBN: 9780415125994. [Preview with Google Books ] ↗
    Listed reading
  • SES #: 1 · READINGS: Propositional Syntax and Semantics, pp. 3–13.
    Reading assignment
  • SES #: 2 · READINGS: Modal Syntax & Semantics, pp. 13–21, R.
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  • SES #: 3 · READINGS: Our “Base” Modal Logic K, pp. 23–33.
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  • SES #: 4 · READINGS: Duality in K, pp. 33–36.
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  • SES #: 5 · READINGS: Soundness of K, pp. 36–41.
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  • SES #: 6 · READINGS: Systems T and D (for Deontic), pp. 41–50.
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  • SES #: 7 · READINGS: Systems S4, B, and S5, pp. 51–64.
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  • SES #: 8 · READINGS: Semantic Diagrams, pp. 72–84.
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  • SES #: 9 · READINGS: Application to S4 and S5, pp. 85–92.
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  • SES #: 10 · READINGS: Completeness and Consistency, pp. 111–9.
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  • SES #: 11 · READINGS: Completeness of K, T, B, S4, and S5, pp. 119–21.
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  • SES #: 12 · READINGS: Dynamic Logic. Neighborhood Semantics, and Lewis’s Counterfactuals, pp. 220–24, R.
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  • SES #: 13 · READINGS: Syntactic Modality and Probabilistic Semantics, pp. 225–8, R.
    Reading assignment
  • SES #: 14 · READINGS: Regular and Modal Predicate Calculus, pp. 235–50.
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  • SES #: 15 · READINGS: De Re and De Dicto, pp. 250–54.
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  • SES #: 16 · READINGS: Canonical Models, pp. 256–62.
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  • SES #: 17 · READINGS: Completeness and Decidability, pp. 262–5 and 271–2.
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  • SES #: 18 · READINGS: The Barcan Formula, pp. 274–83.
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  • SES #: 19 · READINGS: The Converse Barcan Formula, pp. 289–92.
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  • SES #: 20 · READINGS: Existence Predicates and Possibilist Quantification, pp. 292–6 and 303–4.
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  • SES #: 21 · READINGS: Identity, pp. 312–7.
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  • SES #: 22 · READINGS: Descriptions and Scope, pp. 318–26.
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  • SES #: 23 · READINGS: Contingent Identity, pp. 330–35, R.
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  • SES #: 24 · READINGS: Unaxiomatizability of Plenitude, pp. 335–42.
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  • SES #: 25 · READINGS: Intensional Objects and the Sense-reference Distinction, pp. 342–6.
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  • SES #: 26 · READINGS: First-order Modal Theories and Actuality, pp. 349–53, R.
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  • SES #: 27 · READINGS: Counterpart Theory, pp. 353–8, R.
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Prerequisites & course information

Prereq: 24.141 U (Spring) 3-0-9 units. HASS-H

Sources