PhD scholarship "Modal Logic, Foundations of Equilibrium Logic and Answer Set Programming"

[Andreas Herzig]

PhD scholarship "Modal Logic, Foundations of Equilibrium Logic and 
Answer Set Programming"

Answer Set Programming (ASP) is a successful new paradigm for 
declarative programming and logic-based problem solving. Recent research 
has focused on language extensions of ASP (e.g. by epistemic and 
temporal concepts) and on the development of logical techniques for 
program analysis and modularity.

Non-classical logics such as equilibrium logic [Lifschitz et al. 2001] 
are now widely acknowledged to form an adequate logical foundation for 
ASP. Recently it has been proposed to recast equilibrium logic in the 
framework of modal logic [Farinas and Herzig 2011].

The aim of the thesis is to further strengthen the connections between 
ASP and modal logic. Some of the areas that could be developed during 
the thesis are:
- modal logics contributing to the foundations of ASP;
- extensions of equilibrium logic with modal operators of time, 
knowledge, belief, etc.;
- hybrid knowledge bases that combine reasoning with nonmonotonic rules 
and classical knowledge sources such as ontologies.

The thesis will be prepared in the European Lab "Advanced Studies in 
Information Representation and Processing" in co-tutorship between 
Institut de Recherche en Informatique de Toulouse (IRIT) and Universidad 
Politecnica de Madrid (UPM). It starts on October 1, 2011. The 
scholarship is provided by the French Ministery of Education (3 years, 
about 1600€ per month).

References:
[Farinas and Herzig 2011] L. Fariñas del Cerro and A. Herzig, "The modal 
logic of equilibrium models", Proc. Frontiers of Combining Systems 
(FroCoS 2011), to appear.
[Lifschitz et al. 2001] V. Lifschitz and D. Pearce and A. Valverde, 
"Strongly equivalent logic programs", ACM Transactions on Computational 
Logic 2 (4), pp. 526-541. 2001. (see http://www.equilibriumlogic.net)

Supervisors:
Andreas Herzig and Luis Farinas del Cerro (IRIT), David Pearce (UPM)

Required competences:
Applicants should have some knowledge of modal logic and/or ASP.

Applicants should send a CV (including grades) to herzig at irit.fr and 
farinas at irit.fr before July 10, 2011.