Partiality and games: propositional logic

Gabriel Sandu, A Pietarinen

Research output: Contribution to journalJournal articlepeer-review


We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is generated as a property of non-determinacy of games. Over-defined values are produced by adding a weak, contradictory negation or, alternatively, by relaxing the assumption that games are strictly competitive. In general, particular forms of extensive imperfect information games give rise to a generalised propositional logic where various forms of informational dependencies and independencies of connectives can be studied.
Original languageEnglish
Pages (from-to)101-121
Number of pages21
JournalLogic Journal of the IGPL
Issue number1
Publication statusPublished - 1 Jan 2001

User-Defined Keywords

  • Partiality
  • transjunction
  • game-theoretic semantics
  • imperfect information
  • extensive form games
  • determinacy


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