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106
Fresh Logic
 Journal of Applied Logic
, 2007
"... Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with resp ..."
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Cited by 186 (21 self)
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Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with respect to metavariables. We present oneandahalfthorder logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of oneandahalfthorder logic derivability, show them equivalent, show that the derivations satisfy cutelimination, and prove correctness of an interpretation of firstorder logic within it. We discuss the technicalities in a wider context as a casestudy for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation
Hybrid Logics: Characterization, Interpolation and Complexity
 Journal of Symbolic Logic
, 1999
"... Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(#; @). We sho ..."
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Cited by 101 (35 self)
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Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(#; @). We show in detail that H(#; @) is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of EhrenfeuchtFrasse game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that H(#; @) corresponds to the fragment of rstorder logic which is invariant for generated submodels. We then show that H(#; @) enjoys (strong) interpolation, provide counterexamples for its nite variable fragments, and show that weak interpolation holds for the sublanguage H(@). Finally, we provide complexity results for H(@) and other fragments and variants, and sh...
'One is a Lonely Number': on the logic of communication
, 2002
"... Logic is not just about singleagent notions like reasoning, or zeroagent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied ..."
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Cited by 66 (17 self)
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Logic is not just about singleagent notions like reasoning, or zeroagent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied systematically by merging epistemic and dynamic logic.
Dynamic Epistemic Logic
 Logic, Language, and Information 2, Stanford University, CSLI Publication
, 1997
"... This paper is the result of combining two traditions in formal logic: epistemic logic and dynamic semantics. Dynamic semantics is a branch of formal semantics that is concerned with ..."
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Cited by 36 (1 self)
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This paper is the result of combining two traditions in formal logic: epistemic logic and dynamic semantics. Dynamic semantics is a branch of formal semantics that is concerned with
A modal walk through space
 JOURNAL OF APPLIED NONCLASSICAL LOGICS
, 2002
"... We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new finestructure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and ..."
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Cited by 32 (5 self)
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We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new finestructure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering of interesting new questions.
Complexity of Modal Logics of Relations
, 1997
"... We consider two families of modal logics of relations: arrow logic and cylindric modal logic and several natural expansions of these, interpreted on a range of (relativised) modelclasses. We give a systematic study of the complexity of the validity problem of these logics, obtaining price tags for ..."
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Cited by 24 (9 self)
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We consider two families of modal logics of relations: arrow logic and cylindric modal logic and several natural expansions of these, interpreted on a range of (relativised) modelclasses. We give a systematic study of the complexity of the validity problem of these logics, obtaining price tags for various features as assumptions on the universe of the models, similarity types, and number of variables involved. The general picture is that the process of relativisation turns an undecidable logic into one whose validity problem is exptimecomplete. There are interesting deviations to this though, which we also discuss. The numerous results in this paper are all directed to obtain a better understanding why relativisation can turn an undecidable modal logic of relations into a decidable one. We connect the semantic way of "taming logic" by relativisation with the syntactic approach of isolating decidable socalled guarded fragments by showing that validity of loosely guarded formulas is p...
The Geometry of Knowledge
 IN ASPECTS OF UNIVERSAL LOGIC, VOLUME 17 OF TRAVAUX LOG
, 2004
"... The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multiagent epistemic language, whose main uses so far have been in ..."
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Cited by 23 (7 self)
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The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multiagent epistemic language, whose main uses so far have been in reasoning about space. We show that this more geometrical perspective affords greater powers of distinction in the study of common knowledge, defining new collective agents, and merging information for groups of agents.
Tolerance Logic
 Journal of Logic, Language and Information
, 1999
"... . We expand rst order models with a tolerance relation on the domain. Intuitively, two elements stand in this relation if they are \cognitively close" for the agent who holds the model. This simple notion turns out to be very powerful. It leads to a semantic characterization of the guarded fragment ..."
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Cited by 20 (4 self)
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. We expand rst order models with a tolerance relation on the domain. Intuitively, two elements stand in this relation if they are \cognitively close" for the agent who holds the model. This simple notion turns out to be very powerful. It leads to a semantic characterization of the guarded fragment of Andreka, van Benthem and Nemeti, and highlights the strong analogies between modal logic and this fragment. Viewing the resulting logic tolerance logic dynamically it is a resource{conscious information processing alternative to classical rst order logic. The dierences are indicated by several examples. Keywords: Guarded fragments, Relativised rst order logic 1. Introduction Out of the joint work of Johan van Benthem and the Hungarian group round Hajnal Andreka, Istvan Nemeti and Ildiko Sain and their PhD students, two approaches for taming a logic evolved. With taming a logic we mean changing the logic in such a way that it becomes decidable. For rst order logic, they too...
Rational Dynamics and Epistemic Logic in Games
, 2002
"... I propose a barebones look at epistemic models for games, with a focus on update procedures for reaching equilibrium 'zones'. Connections are given with standard update and fixedpoint logics. This is just a 'methods' paper, as readers will want to play with models, uncertainty relations, and announ ..."
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Cited by 20 (5 self)
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I propose a barebones look at epistemic models for games, with a focus on update procedures for reaching equilibrium 'zones'. Connections are given with standard update and fixedpoint logics. This is just a 'methods' paper, as readers will want to play with models, uncertainty relations, and announcements different from those used here for the purposes of illustration.