Article

Journal of Philosophical Logic

, Volume 37, Issue 4, pp 387-406

First online:

ALTERNATIVE AXIOMATICS AND COMPLEXITY OF DELIBERATIVE STIT THEORIES

  • Philippe BalbianiAffiliated withInstitut de Recherche en Informatique de Toulouse (IRIT) Email author 
  • , Andreas HerzigAffiliated withInstitut de Recherche en Informatique de Toulouse (IRIT)
  • , Nicolas TroquardAffiliated withInstitut de Recherche en Informatique de Toulouse (IRIT)

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Abstract

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT.

Key words

axiomatization complexity logic of agency STIT