Studia Logica

, Volume 69, Issue 1, pp 133–169 | Cite as

Term-Modal Logics

  • Melvin Fitting
  • Lars Thalmann
  • Andrei Voronkov


Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.

To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators.

This gives us a flexible and uniform language for reasoning about the agents themselves and their knowledge. This article gives examples of the expressiveness of the languages and provides sequent-style and tableau-based proof systems for the logics. Furthermore we give proofs of soundness and completeness with respect to the possible world semantics.

Modal logic multi-agents epistemic logic completeness tableaux 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Melvin Fitting
    • 1
  • Lars Thalmann
    • 2
  • Andrei Voronkov
    • 3
  1. 1.City University of New YorkUSA
  2. 2.Uppsala UniversitySpain
  3. 3.University of ManchesterUkraine

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