Modal Logic
Garson (James)
Source: Stanford Encyclopaedia of Philosophy, 2000-9
Paper - Abstract

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Author’s Abstract

A modal1 is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic2 is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’. However, the term ‘modal logic’3 may be used more broadly for a family of related systems. These include logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as ‘it is obligatory that’ and ‘it is permitted that’, and many others. An understanding of modal logic4 is particularly valuable in the formal analysis of philosophical argument, where expressions from the modal5 family are both common and confusing. Modal logic6 also has important applications in computer science.

  1. What is Modal Logic7?
  2. Modal Logics8
  3. Deontic Logics
  4. Temporal Logics
  5. Conditional Logics
  6. Possible Worlds Semantics
  7. Modal9 Axioms and Conditions on Frames
  8. Map of the Relationships Between Modal Logics10
  9. The General Axiom
  10. Provability Logics
  11. Advanced Modal Logic11
  12. Bisimulation
  13. Quantifiers in Modal Logic12
    Other Internet Resources
    Related Entries


First published Tue Feb 29, 2000; substantive revision Fri Oct 2, 2009; see Stanford Archive: Modal Logic.

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