Workshop description

Three-valued logics have been an object of extensive study since at least the work of Lukasiewicz, with applications to a wide range of natural language phenomena, including presupposition, conditionals and vagueness. While many-valued logics can be studied on their own, there has been a regain of interest for three-valued logics in recent years, with the emergence of new perspectives regarding their applicability to natural language.

In the theory of presupposition projection, in particular, the question of whether the projection of presupposition can be dealt with by means of a trivalent truth-functional semantics has been the object of renewed attention, in particular because truth-functional trivalent approaches appear as a main competitor to both dynamic and pragmatic approaches (viz. Beaver and Krahmer 2001, George 2008, Fox 2008, all of them giving special attention to so-called middle-Kleene logic proposed by Peters, and the recent debates with Schlenker). In the area of vagueness, ways have been proposed to combine the canonical paracomplete and paraconsistent three-valued logics of Kleene and Priest in order to deal with the paradoxes of vagueness, and to account for phenomena such as meaning coarsening and strengthening (viz. Avron et Konikowska 2008,
Cobreros et al. 2010). In the literature on conditionals, finally, the question remains largely open of the selection between a wide range of candidates for the definition of a suitable three-valued conditional (viz. Bradley 2002, Cantwell 2008, Huitink 2009, Rothschild 2009). From a more foundational point of view, finally, the meaning attached to the third truth value can vary significantly depending on the problem under consideration and the definition of logical consequence considered to be relevant.

The aim of this workshop is to solicit new contributions for the extension of two-valued logic with a third truth-value. Submissions are encouraged on logical and linguistics aspects of the use of 3-valued logics, with relevance on the following topics:

- applications of trivalent logic to quantification in natural language
- trivalent logics for conditionals / vagueness / presupposition
- are vagueness and presupposition susceptible of a unified treatment in trivalent logic?
- logical consequence and proof-theory for three-valued logic
- unification and classification of 3-valued logics
- connection between 3-valued logics and other non-classical logics
- partial 2-valued logics vs. 3-valued logics

- do we need more than three truth-values? can we dispense with a third truth value?

Invited speakers

Arnon Avron
Katrin Schulz       
Grzegorz Malinowski

Submission details

Please send your submission in PDF format, at most 10 pages. The recommended submission style is LNCS style, 10 pts, bibliography included see
If needed due to space reasons, technical material such as proofs may be added in an appendix of at most 5 pages. The PDF files have to be uploaded online via the workshop’s submission website:

The author notification date is April 20, 2012 (note the shift of a few days). Prior to the workshop, speakers will have the opportunity to submit an extended abstract for inclusion in the ESSLLI proceedings (deadline June 1, 2012). All participants must register for ESSLLI.

We are working to arrange for a special journal issue to publish revised and extended versions of the best conference papers.

Deadline for submission

Deadline extension: March 17, 2012

Programme committee

Arnon Avron
Pablo Cobreros
Paul Egré (co-chair)
Janneke Huitink
Grzegorz Malinowski
David Ripley (co-chair)
Robert van Rooij


  • European Research Council (FP7/2007-2013) / ERC Advanced Grant agreement n°229 441-CCC (CPR project, directed by F. Récanati)


 Submissions closed