Journal of Philosophical Logic

, Volume 47, Issue 2, pp 325–363 | Cite as

Combinatorial Bitstring Semantics for Arbitrary Logical Fragments

  • Lorenz Demey
  • Hans Smessaert


Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings to arbitrary finite fragments of formulas in arbitrary logical systems, and to study the logical and combinatorial properties of this technique. It is based on the partition of logical space that is induced by a given fragment, and sheds new light on a number of interesting issues, such as the logic-dependence of the Aristotelian relations and the subtle interplay between the Aristotelian and Boolean structure of logical fragments. Finally, the bitstring technique also allows us to systematically analyze fragments from contemporary logical systems, such as public announcement logic, which could not be done before.


Bitstrings Combinatorial semantics Aristotelian diagram Boolean algebra Existential import Public announcement logic 



Thanks to Jan Heylen, Alessio Moretti, Fabien Schang, Margaux Smets and an anonymous referee for their comments on earlier versions of this paper. The first author holds a Postdoctoral Fellowship of the Research Foundation – Flanders (FWO).


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Center for Logic and Analytic PhilosophyKU LeuvenLeuvenBelgium
  2. 2.Research Group on Formal and Computational LinguisticsKU LeuvenLeuvenBelgium

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