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Modal and Guarded Characterisation Theorems over Finite Transition Systems
 In Proceedings LICS 2002
, 2002
"... We explore the nite model theory of the characterisation theorems for modal and guarded fragments of rstorder logic over transition systems and relational structures of width two. Apart from simplifying Rosen's proof of the nite model theory version of van Benthem's classical modal cha ..."
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Cited by 25 (14 self)
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We explore the nite model theory of the characterisation theorems for modal and guarded fragments of rstorder logic over transition systems and relational structures of width two. Apart from simplifying Rosen's proof of the nite model theory version of van Benthem's classical modal characterisation theorem, we employ new techniques to capture analogous characterisations of modal logic with universal and inverse modalities. The analysis rests on Gaifman's locality theorem for rstorder logic together with a natural combinatorial construction of nite, locally acyclic covers for nite transition systems. These techniques carry over to the analysis guarded bisimulation invariance: over nite relational structures of width two, the guarded fragment precisely captures those properties that are rstorder denable and invariant under guarded bisimulation. It remains open whether a full analogue of the guarded characterisation theorem of Andreka, van Benthem and Nemeti, for relational structures of width greater than two, is also valid in the sense of nite model theory. keywords: nite model theory, modal logic, guarded fragment, bisimulation, preservation and characterisation theorems 1
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 frag ..."
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Cited by 22 (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...
Local Normal Forms for FirstOrder Logic with Applications to Games and Automata
 DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1998
"... ..."
Some Aspects of Model Theory and Finite Structures
, 2002
"... this paper is to highlight some of these aspects of the model theory of nite structures, where the nite and in nite interact fruitfully, in order to dispel the perhaps too common perception that ( rstorder) model theory has little to say about nite structures ..."
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Cited by 9 (0 self)
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this paper is to highlight some of these aspects of the model theory of nite structures, where the nite and in nite interact fruitfully, in order to dispel the perhaps too common perception that ( rstorder) model theory has little to say about nite structures
When is Naïve Evaluation Possible?
"... The term naïve evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, i.e., to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when n ..."
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Cited by 6 (3 self)
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The term naïve evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, i.e., to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when naïve evaluation computes them: i.e., when certain answers can be found without inventingnew specialized algorithms. For relational databases it is well known that unions of conjunctive queries possess this desirable property, and results on preservation of formulae under homomorphisms tell us that within relational calculus, this class cannot be extended under the openworld assumption. Our goal here is twofold. First, we develop a general
Guarded Quantification in Least Fixed Point Logic
, 2002
"... We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point ..."
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Cited by 2 (1 self)
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We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But guarding quantification increases worstcase time complexity.
ANaı̈ve Evaluation of Queries over Incomplete Databases
"... The term näıve evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, i.e., to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when ..."
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Cited by 1 (1 self)
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The term näıve evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, i.e., to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when näıve evaluation computes them: i.e., when certain answers can be found without inventing new specialized algorithms. For relational databases it is well known that unions of conjunctive queries possess this desirable property, and results on preservation of formulae under homomorphisms tell us that within relational calculus, this class cannot be extended under the openworld assumption. Our goal here is twofold. First, we develop a general framework that allows us to determine, for a given semantics of incompleteness, classes of queries for which näıve evaluation computes certain answers. Second, we apply this approach to a variety of semantics, showing that for many classes of queries beyond unions of conjunctive queries, näıve evaluation makes perfect sense under assumptions different from openworld. Our key observations are: (1) näıve evaluation is equivalent to monotonicity of queries with respect to a semanticsinduced ordering, and (2) for most reasonable semantics of incompleteness, such monotonicity is captured by preservation under various types of homomorphisms. Using these results we find classes of queries for which näıve evaluation works, e.g., positive firstorder formulae for the closedworld semantics.
Application of logic to combinatorial sequences and their recurrence relations
 In Model Theoretic Methods in Finite Combinatorics, volume 558 189  Computer Science Department  Ph.D. Thesis PHD201211  2012 of Contemporary Mathematics
, 2011
"... 1. Sequences of integers and their combinatorial interpretations 2. Linear recurrences 3. Logical formalisms 4. Finiteness conditions ..."
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1. Sequences of integers and their combinatorial interpretations 2. Linear recurrences 3. Logical formalisms 4. Finiteness conditions
Datalog Queries Distributing over Components
"... We investigate the class D of queries that distribute over components. These are the queries that can be evaluated by taking the union of the query results over the connected components of the database instance. We show that it is undecidable whether a (positive) Datalog program distributes over com ..."
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We investigate the class D of queries that distribute over components. These are the queries that can be evaluated by taking the union of the query results over the connected components of the database instance. We show that it is undecidable whether a (positive) Datalog program distributes over components. Additionally, we show that connected Datalog ¬ (the fragment of Datalog ¬ where all rules are connected) provides an effective syntax for Datalog ¬ programs that distribute over components under the stratified as well as under the wellfounded semantics. As a corollary, we obtain a simple proof for one of the main results in previous work [19], namely, that the classic winmove query is in F2 (a particular class of coordinationfree queries).
Model Theory in Computer Science: My own recurrent themes
, 2011
"... I review my own experiences in research and the management of science. ..."