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Philippe Balbiani

Publications and source records attributed to Philippe Balbiani.

26 records · Page 2Linked to original sources
arXiv2019

About the unification type of simple symmetric modal logics

The unification problem in a normal modal logic is to determine, given a formula F, whether there exists a substitution s such that s(F) is in that logic. In that case, s is a unifier of F. We shall say that a set of unifiers of a unifiable formula F is complete if for all unifiers s of F, there exists a unifier t of F in that set such that t is more general than s. When a unifiable formula has no minimal complete set of unifiers, the formula is nullary. In this paper, we prove that KB, KDB and KTB possess nullary formulas.

cs.LO↗
arXiv2018

Frame-validity games and lower bounds on the complexity of modal axioms

We introduce frame-equivalence games tailored for reasoning about the size, modal depth, number of occurrences of symbols and number of different propositional variables of modal formulae defining a given frame-property. Using these games, we prove lower bounds on the above measures for a number of well-known modal axioms; what is more, for some of the axioms, we show that they are optimal among the formulae defining the respective class of frames.

cs.LO↗
arXiv2018

Bisimulations for intuitionistic temporal logics

We introduce bisimulations for the logic $ITL^e$ with `next', `until' and `release', an intuitionistic temporal logic based on structures equipped with a partial order used to interpret intuitionistic implication and a monotone function used to interpret the temporal modalities. Our main results are that `eventually', which is definable in terms of `until', cannot be defined in terms of `next' and `henceforth', and similarly that `henceforth', definable in terms of `release', cannot be defined in terms of `next' and `until', even over the smaller class of here-and-there models.

math.LO↗
arXiv2017

Exploring the bidimensional space: A dynamic logic point of view

We present a family of logics for reasoning about agents' positions and motion in the plane which have several potential applications in the area of multi-agent systems (MAS), such as multi-agent planning and robotics. The most general logic includes (i) atomic formulas for representing the truth of a given fact or the presence of a given agent at a certain position of the plane, (ii) atomic programs corresponding to the four basic orientations in the plane (up, down, left, right) as well as the four program constructs of propositional dynamic logic (sequential composition, nondeterministic composition, iteration and test). As this logic is not computably enumerable, we study some interesting decidable and axiomatizable fragments of it. We also present a decidable extension of the iteration-free fragment of the logic by special programs representing motion of agents in the plane.

cs.AI↗
arXiv2014

DL-PA and DCL-PC: model checking and satisfiability problem are indeed in PSPACE

We prove that the model checking and the satisfiability problem of both Dynamic Logic of Propositional Assignments DL-PA and Coalition Logic of Propositional Control and Delegation DCL-PC are in PSPACE. We explain why the proof of EXPTIME-hardness of the model checking problem of DL-PA presented in (Balbiani, Herzig, Troquard, 2013) is false. We also explain why the proof of membership in PSPACE of the model checking problem of DCL-PC given in (van der Hoek, Walther, Wooldridge, 2010) is wrong.

cs.LO↗
arXiv2014

A simple proof of the completeness of APAL

We provide a simple proof of the completeness of arbitrary public announcement logic APAL. The proof is an improvement over the proof found in the publication Knowable as Known after an Announcement.

cs.LO↗
arXiv2007

Alternative axiomatics and complexity of deliberative STIT theories

We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one 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 the Chellas 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 the Chellas' STIT.

cs.LO↗