A Four-Valued Hybrid Logic with Non-dual Modal Operators

  • Diana CostaEmail author
  • Manuel A. Martins
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12005)


Hybrid logics are an extension of modal logics where it is possible to refer to a specific state, thus allowing the description of what happens at specific states, equalities and transitions between them. This makes hybrid logics very desirable to work with relational structures.

However, as the amount of information grows, it becomes increasingly more common to find inconsistencies. Information collected about a particular hybrid structure is not an exception. Rather than discarding all the data congregated, working with a paraconsistent type of logic allows us to keep it and still make sensible inferences.

In this paper we introduce a four-valued semantics for hybrid logic, where contradictions are allowed both at the level of propositional variables and accessibility relations. A distinguishing feature of this new logic is the fact that the classical equivalence between modal operators will be broken. A sound and complete tableau system is also presented.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity College LondonLondonEngland
  2. 2.CIDMA – Department of MathematicsUniversity of AveiroAveiroPortugal

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