58 found
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  1.  97
    'Knowable' as 'Known After an Announcement'.Philippe Balbiani, Alexandru Baltag, Hans van Ditmarsch, Andreas Herzig, Tomohiro Hoshi & Tiago de Lima - 2008 - Review of Symbolic Logic 1 (3):305-334.
    Public announcement logic is an extension of multiagent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: after which , does it hold that Kφ? We give various semantic results and show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.
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  2.  75
    Alternative Axiomatics and Complexity of Deliberative Stit Theories.Philippe Balbiani, Andreas Herzig & Nicolas Troquard - 2008 - Journal of Philosophical Logic 37 (4):387 - 406.
    We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and 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 Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...)
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  3.  19
    KD is Nullary.Philippe Balbiani & Çiğdem Gencer - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):196-205.
    In the ordinary modal language, KD is the modal logic determined by the class of all serial frames. In this paper, we demonstrate that KD is nullary.
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  4.  15
    Unification in Epistemic Logics.Philippe Balbiani & Çiğdem Gencer - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):91-105.
    Epistemic logics are essential to the design of logical systems that capture elements of reasoning about knowledge. In this paper, we study the computability of unifiability and the unification types in several epistemic logics.
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  5.  29
    Group Announcement Logic.Thomas Ågotnes, Philippe Balbiani, Hans van Ditmarsch & Pablo Seban - 2010 - Journal of Applied Logic 8 (1):62-81.
  6.  7
    Remarks About the Unification Type of Several Non-Symmetric Non-Transitive Modal Logics.Philippe Balbiani - 2019 - Logic Journal of the IGPL 27 (5):639-658.
    The problem of unification in a normal modal logic $L$ can be defined as follows: given a formula $\varphi$, determine whether there exists a substitution $\sigma$ such that $\sigma $ is in $L$. In this paper, we prove that for several non-symmetric non-transitive modal logics, there exists unifiable formulas that possess no minimal complete set of unifiers.
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  7.  14
    The Dynamics of Epistemic Attitudes in Resource-Bounded Agents.Philippe Balbiani, David Fernández-Duque & Emiliano Lorini - 2019 - Studia Logica 107 (3):457-488.
    The paper presents a new logic for reasoning about the formation of beliefs through perception or through inference in non-omniscient resource-bounded agents. The logic distinguishes the concept of explicit belief from the concept of background knowledge. This distinction is reflected in its formal semantics and axiomatics: we use a non-standard semantics putting together a neighborhood semantics for explicit beliefs and relational semantics for background knowledge, and we have specific axioms in the logic highlighting the relationship between the two concepts. Mental (...)
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  8.  13
    About the Unification Type of Modal Logics Between.Philippe Balbiani & Çiğdem Gencer - 2020 - Studia Logica 108 (5):941-966.
    The unification problem in a normal modal logic is to determine, given a formula.
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  9. Remarks About the Unification Types of Some Locally Tabular Normal Modal Logics.Philippe Balbiani, ÇiĞdem Gencer, Maryam Rostamigiv & Tinko Tinchev - forthcoming - Logic Journal of the IGPL.
    It is already known that unifiable formulas in normal modal logic $\textbf {K}+\square ^{2}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{2}\bot $ are unitary. In this paper, we prove that for all $d{\geq }3$, unifiable formulas in normal modal logic $\textbf {K}+\square ^{d}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{d}\bot $ are unitary.
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  10.  6
    Relational Representation Theorems for Extended Contact Algebras.Philippe Balbiani & Tatyana Ivanova - 2021 - Studia Logica 109 (4):701-723.
    In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A, B and D if the intersection of A and B is included in D. The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between point-free (...)
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  11.  84
    Modal Logics for Parallelism, Orthogonality, and Affine Geometries.Philippe Balbiani & Valentin Goranko - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):365-397.
    We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.
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  12.  17
    Putting Right the Wording and the Proof of the Truth Lemma for APAL.Philippe Balbiani - 2015 - Journal of Applied Non-Classical Logics 25 (1):2-19.
    is an extension of public announcement logic. It is based on a modal operator that expresses what is true after any arbitrary announcement. An incorrect Truth Lemma has been stated and ‘demonstrated’ in Balbiani et al. . In this paper, we put right the wording and the proof of the Truth Lemma for.
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  13.  56
    The Modal Multilogic of Geometry.Philippe Balbiani - 1998 - Journal of Applied Non-Classical Logics 8 (3):259-281.
    ABSTRACT A spatial logic is a modal logic of which the models are the mathematical models of space. Successively considering the mathematical models of space that are the incidence geometry and the projective geometry, we will successively establish the language, the semantical basis, the axiomatical presentation, the proof of the decidability and the proof of the completeness of INC, the modal multilogic of incidence geometry, and PRO, the modal multilogic of projective geometry.
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  14.  2
    Frame-Validity Games and Lower Bounds on the Complexity of Modal Axioms.Philippe Balbiani, David Fernández-Duque, Andreas Herzig & Petar Iliev - 2022 - Logic Journal of the IGPL 30 (1):155-185.
    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.
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  15.  18
    Propositional Dynamic Logic.Philippe Balbiani - 2008 - Stanford Encyclopedia of Philosophy.
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  16. Definability and Computability for PRSPDL.Philippe Balbiani & Tinko Tinchev - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 16-33.
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  17.  1
    Unification in Modal Logic Alt1.Philippe Balbiani & Tinko Tinchev - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 117-134.
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  18.  3
    Every World Can See a Sahlqvist World.Philippe Balbiani, I. Shapirovsky & V. Shshtman - 2006 - In Guido Governatori, Ian Hodkinson & Yde Venema (eds.), Advances in Modal Logic, Volume 6. CSLI Publications. pp. 69-85.
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  19.  4
    Before Announcement.Philippe Balbiani, Hans van Ditmarsch & Andreas Herzig - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 58-77.
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  20.  3
    Reasoning About Negligibility and Proximity in the Set of All Hyperreals.Philippe Balbiani - 2016 - Journal of Applied Logic 16:14-36.
  21.  24
    PDL with Intersection of Programs: A Complete Axiomatization.Philippe Balbiani & Dimiter Vakarelov - 2003 - Journal of Applied Non-Classical Logics 13 (3-4):231-276.
    One of the important extensions of PDL is PDL with intersection of programs. We devote this paper to its complete axiomatization.
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  22.  65
    Complete Axiomatization of a Relative Modal Logic with Composition and Intersection.Philippe Balbiani & Luis Fariñas del Cerro - 1998 - Journal of Applied Non-Classical Logics 8 (4):325-335.
    ABSTRACT We consider the question of the complete axiomatization of a relative modal logic with composition and intersection.
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  23.  2
    Every World Can See a Sahlqvist World.Philippe Balbiani, I. Shapirovsky & V. Shshtman - 2006 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 69-85.
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  24.  13
    Dynamic Logics of the Region-Based Theory of Discrete Spaces.Philippe Balbiani, Tinko Tinchev & Dimiter Vakarelov - 2007 - Journal of Applied Non-Classical Logics 17 (1):39-61.
    The aim of this paper is to give new kinds of modal logics suitable for reasoning about regions in discrete spaces. We call them dynamic logics of the region-based theory of discrete spaces. These modal logics are linguistic restrictions of propositional dynamic logic with the global diamond E. Their formulas are equivalent to Boolean combinations of modal formulas like E where A and B are Boolean terms and α is a relational term. Examining what we can say about dynamic models (...)
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  25.  18
    A Hierarchy of Modal Logics with Relative Accessibility Relations.Philippe Balbiani & Ewa Orlowska - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):303-328.
    ABSTRACT In this paper we introduce and investigate various classes of multimodal logics based on frames with relative accessibility relations. We discuss their applicability to representation and analysis of incomplete information. We provide axiom systems for these logics and we prove their completeness.
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  26.  16
    Foreword.Philippe Balbiani - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):317-318.
  27.  36
    A New Proof of Completeness for a Relative Modal Logic with Composition and Intersection.Philippe Balbiani - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):269-280.
    This paper is devoted to the completeness issue of RMLCI — the relative modal logic with composition and intersection— a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally definable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper “Complete axiomatization of a relative modal logic with composition and intersection”. The theorem asserts that the proof theory of RMLCI is (...)
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  28.  8
    Line-Based Affine Reasoning in Euclidean Plane.Philippe Balbiani & Tinko Tinchev - 2007 - Journal of Applied Logic 5 (3):421-434.
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  29.  2
    About Intuitionistic Public Announcement Logic.Philippe Balbiani & Didier Galmiche - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 97-116.
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  30.  29
    Axiomatization and Completeness of Lexicographic Products of Modal Logics.Philippe Balbiani - 2011 - Journal of Applied Non-Classical Logics 21 (2):141-176.
    This paper sets out a new way of combining Kripke-complete modal logics: lexicographic product. It discusses some basic properties of the lexicographic product construction and proves axiomatization/completeness results.
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  31.  67
    A Relational Model of Movement.Philippe Balbiani & Fariñas del Cerro - forthcoming - Logique Et Analyse.
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  32.  8
    Dynamic Extensions of Arrow Logic.Philippe Balbiani & Dimiter Vakarelov - 2004 - Annals of Pure and Applied Logic 127 (1-3):1-15.
    This paper is devoted to the complete axiomatization of dynamic extensions of arrow logic based on a restriction of propositional dynamic logic with intersection. Our deductive systems contain an unorthodox inference rule: the inference rule of intersection. The proof of the completeness of our deductive systems uses the technique of the canonical model.
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  33.  51
    Modal Logics for Reasoning About Infinite Unions and Intersections of Binary Relations.Natasha Alechina, Philippe Balbiani & Dmitry Shkatov - 2012 - Journal of Applied Non-Classical Logics 22 (4):275 - 294.
    (2012). Modal logics for reasoning about infinite unions and intersections of binary relations. Journal of Applied Non-Classical Logics: Vol. 22, No. 4, pp. 275-294. doi: 10.1080/11663081.2012.705960.
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  34.  9
    Inequality Without Irreflexivity.Philippe Balbiani - 1999 - Journal of Applied Non-Classical Logics 9 (4):523-534.
    ABSTRACT This paper presents the axioinatization—without the rule of irreflexivity—of the modal logic of inequality as well as a method for proving its completeness. This method uses the technics of the frame of subordination.
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  35. Unification Types in Euclidean Modal Logics.Majid Alizadeh, Mohammad Ardeshir, Philippe Balbiani & Mojtaba Mojtahedi - forthcoming - Logic Journal of the IGPL.
    We prove that $\textbf {K}5$ and some of its extensions that do not contain $\textbf {K}4$ are of unification type $1$.
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  36. Advances in Modal Logic, Volume 4: Papers From the Fourth Aiml Conference, Held in Toulouse, October 2002.Philippe Balbiani, Nobu-Yuki Suzuki & Frank Wolter (eds.) - 2003 - London, England: King's College Publications.
  37. Orthogonal Frames and Indexed Relations.Philippe Balbiani & Saúl Fernández González - 2021 - In Alexandra Silva, Renata Wassermann & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 219-234.
    We define and study the notion of an indexed frame. This is a bi-dimensional structure consisting of a Cartesian product equipped with relations which only relate pairs if they coincide in one of their components. We show that these structures are quite ubiquitous in modal logic, showing up in the literature as products of Kripke frames, subset spaces, or temporal frames for STIT logics. We show that indexed frames are completely characterised by their ‘orthogonal’ relations, and we provide their sound (...)
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  38. Reasoning About Vague Concepts in the Theory of Property Systems.Philippe Balbiani - 2004 - Logique Et Analyse 47:445.
     
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  39. Terminological Modal Logic.Philippe Balbiani - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 1. CSLI Publications. pp. 23-39.
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  40. Terminological Modal Logic.Philippe Balbiani - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 23-39.
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  41.  21
    Foreword.Philippe Balbiani, Luis Fariñas Del Cerro & Andreas Herzig - 2010 - Journal of Applied Non-Classical Logics 20 (3):138-138.
  42.  13
    Hyper Arrow Logic with Indiscernibility and Complementarity.Philippe Balbiani - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):137-152.
    In this paper, we study indiscernibility relations and complementarity relations in hyper arrow structures. A first-order characterization of indiscernibility and complementarity is obtained through a duality result between hyper arrow structures and certain structures of relational type characterized by first-order conditions. A modal analysis of indiscernibility and complementarity is performed through a modal logic which modalities correspond to indiscernibility relations and complementarity relations in hyper arrow structures.
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  43.  5
    Two Decision Problems in Contact Logics.Philippe Balbiani, Çiğdem Gencer & Zafer Özdemir - 2019 - Logic Journal of the IGPL 27 (1):8-32.
    Contact Logics provide a natural framework for representing and reasoning about regions in several areas of computer science. In this paper, we focus our attention on reasoning methods for Contact Logics and address the satisfiability problem and the unifiability problem. Firstly, we give sound and complete tableaux-based decision procedures in Contact Logics and we obtain new results about the decidability/complexity of the satisfiability problem in these logics. Secondly, we address the computability of the unifiability problem in Contact Logics and we (...)
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  44.  10
    Foreword.Philippe Balbiani & Tinko Tinchev - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):135-135.
  45.  9
    Foreword.Philippe Balbiani, Hans van Ditmarsch & Jan van Eijck - 2009 - Journal of Applied Non-Classical Logics 19 (4):397-402.
  46.  9
    Foreword.Philippe Balbiani - 2005 - Journal of Applied Non-Classical Logics 15 (2):113-114.
  47.  6
    Axiomatizing the Lexicographic Products of Modal Logics with Linear Temporal Logics.Philippe Balbiani & David Fernández-Duque - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 78-96.
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  48.  6
    An Expressive Two-Sorted Spatial Logic for Plane Projective Geometry.Philippe Balbiani - 2006 - In Guido Governatori, Ian Hodkinson & Yde Venema (eds.), Advances in Modal Logic, Volume 6. CSLI Publications. pp. 49-68.
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  49.  3
    Unification with Parameters in the Implication Fragment of Classical Propositional Logic.Philippe Balbiani & Mojtaba Mojtahedi - forthcoming - Logic Journal of the IGPL.
    In this paper, we show that the implication fragment of classical propositional logic is finitary for unification with parameters.
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  50.  3
    An Expressive Two-Sorted Spatial Logic for Plane Projective Geometry.Philippe Balbiani - 2006 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 49-68.
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