Searcharxiv⌕ Search

arXiv subjects

Olivier Gasquet

Publications and source records attributed to Olivier Gasquet.

7 recordsLinked to original sources
arXiv2026

Parameterized complexity of n-dense modal logics

Exact tight bounds of the complexity of the satisfiability problem for dense modal logics is a difficult question, likely somewhere between $\PSPACE$ and $\EXPSPACE$ depending of the logic under question. For a class of them, called here $n$-dense logics (characterized by axioms $\Box^n p\rightarrow \Box p$), we refine the known results -- membership in $\NEXPTIME$ -- in the light of parameterized complexity, as introduced in \cite{Downey}, and prove that they belong to the parameterized class para-$\PSPACE$: there exists a poly-space algorithm once the modal depth of the input is considered as a parameter. This is done by generalizing the novel analysis tool introduced in \cite{BalGasq25}, and therein called windows, to \emph{recursive windows}.

cs.LO↗
arXiv2025

Recursive windows for grammar logics of bounded density

We introduce the family of multi-modal logics of bounded density and with a tableau-like approach using finite \emph{windows} which were introduced in \cite{BalGasq25} and that we generalize to recursive windows. We prove that their satisfiability problem is {\bfseries PSPACE}-complete. As a side effect, the monomodal logic of density is shown to be in para-{\bfseries PSPACE}.

cs.LO↗
arXiv2025

PSPACE-completeness of bimodal transitive weak-density logic

Windows have been introduce in \cite{BalGasq25} as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the ``folklore'' case of bimodal $\K4$ already treated in \cite{Halpern} but which is worth a fresh review, we show that windows allow to polynomially solve the satisfiability problem when adding transitivity to weak-density, by mixing algorithms for bimodal K together with windows-approach. The conclusion is that both satisfiability and validity are PSPACE-complete for these logics.

cs.LO↗
arXiv2025

Complexity of some modal logics of density (extended version)

By using a selective filtration argument, we prove that the satisfiability problem of the unimodal logic of density is in $EXPTIME$. By using a tableau-like approach, we prove that the satisfiability problem of the bimodal logic of weak density is in $PSPACE$.

cs.LO↗
arXiv2015

Twist your logic with TouIST

SAT provers are powerful tools for solving real-sized logic problems, but using them requires solid programming knowledge and may be seen w.r.t.\ logic like assembly language w.r.t.\ programming. Something like a high level language was missing to ease various users to take benefit of these tools. {\sc \texttt {TouIST}}\ aims at filling this gap. It is devoted to propositional logic and its main features are 1) to offer a high-level logic langage for expressing succintly complex formulas (e.g.\ formulas describing Sudoku rules, planification problems,\ldots) and 2) to find models to these formulas by using the adequate powerful prover, which the user has no need to know about. It consists in a friendly interface that offers several syntactic facilities and which is connected with some sufficiently powerful provers allowing to automatically solve big instances of difficult problems (such as time-tables or Sudokus). It can interact with various provers: pure SAT solver but also SMT provers (SAT modulo theories - like linear theory of reals, etc) and thus may also be used by beginners for experiencing with pure propositional problems up to graduate students or even researchers for solving planification problems involving big sets of fluents and numerical constraints on them.

cs.CY↗