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18
Foundations of Instance Level Updates in Expressive Description Logics
, 2011
"... In description logic (DL), ABoxes are used for describing the state of affairs in an application domain. We consider the problem of updating ABoxes when the state changes, assuming that update information is described at an atomic level, i.e., in terms of possibly negated ABox assertions that involv ..."
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In description logic (DL), ABoxes are used for describing the state of affairs in an application domain. We consider the problem of updating ABoxes when the state changes, assuming that update information is described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs, in particular addressing questions of expressibility and succinctness: can updated ABoxes always be expressed in the DL in which the original ABox was formulated and, if so, what is the size of the updated ABox? It turns out that DLs have to include nominals and the ‘@’ constructor of hybrid logic for updated ABoxes to be expressible, and that this still holds when updated ABoxes are approximated. Moreover, the size of updated ABoxes is exponential in the role depth of the original ABox and the size of the update. We also show that this situation improves when updated ABoxes are allowed to contain additional auxiliary symbols. Then, DLs only need to include nominals for updated ABoxes to exist, and the size of updated ABoxes is polynomial in the size of both the original ABox and the update.
Knowability from a Logical Point of View
, 2010
"... The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in questio ..."
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The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in question does not change from true to false in the process of discovery, ’ hidden in the verificationist approach. Once stability is made explicit, the resulting stable knowability principle accurately represents verificationist knowability, does not yield the omniscience property, and can be offered as a resolution of the knowability paradox. Two more principles are considered: total knowability stating that it is possible to know whether a proposition holds or not, and monotonic knowability stemming from the intrinsically intuitionistic reading of knowability. The study of these four principles yields a “knowability diamond ” describing their logical strength. These results are obtained within a logical framework which opens the door to the systematic study of knowability from a logical point of view. 1
FOR BETTER OR FOR WORSE: DYNAMIC LOGICS OF PREFERENCE
, 2008
"... In the last few years, preference logic and in particular, the dynamic logic of preference change, has suddenly become a live topic in my Amsterdam and Stanford environments. At the request of the editors, this article explains how this interest came about, and what is happening. I mainly present a ..."
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In the last few years, preference logic and in particular, the dynamic logic of preference change, has suddenly become a live topic in my Amsterdam and Stanford environments. At the request of the editors, this article explains how this interest came about, and what is happening. I mainly present a story around some recent dissertations and supporting papers, which are found in the references. There is no pretense at complete coverage of preference logic (for that, see Hanson 2001) or even of preference change (Hanson 1995).
THE ART OF MODELING
, 2009
"... ‘Possible worlds semantics’ for modal logic is a widely used term, sometimes with ominous metaphysical connotations, but what does this style of modeling involve today? We discuss three main issues, using epistemic logic as a running example, and drawing upon both mathematical results and practices ..."
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‘Possible worlds semantics’ for modal logic is a widely used term, sometimes with ominous metaphysical connotations, but what does this style of modeling involve today? We discuss three main issues, using epistemic logic as a running example, and drawing upon both mathematical results and practices in the expertise of working researchers. Our first question is a foundational one: how does one associate a type of model with a language, and what considerations affect that choice? Our focus is on invariance and definability results, familiar from the mathematical and computational tradition, though less so in philosophy. The second question is less deep, but maybe even more challenging in practice: once we have chosen a type of models for a language, how does one select and then maintain models appropriate to concrete scenarios of application? While there is a lot of ‘art’ to this in the literature, there is very little ‘science’ of model construction for modal logics. We show how this works in dynamic epistemic logics, and identify some current challenges for a true ‘modeling theory’ as opposed to the more abstract usual ‘model theory’. Finally, we discuss the pervasive tension between ‘thin’ and ‘thick ’ worlds in modal logic, using examples from game theory, and pointing out how the contrast can be made fruitful.
A Propositional Dynamic Logic Approach for Order of Magnitude Reasoning?
"... Abstract. We introduce a Propositional Dynamic Logic for order of magnitude reasoning in order to formalize qualitative operations of sum and product. This new logic has enough expressive power to consider, for example, the concept of closeness, and to study some interesting properties for the qual ..."
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Abstract. We introduce a Propositional Dynamic Logic for order of magnitude reasoning in order to formalize qualitative operations of sum and product. This new logic has enough expressive power to consider, for example, the concept of closeness, and to study some interesting properties for the qualitative operations, together with the logical definability of these properties. Moreover, we show the applicability of our approach on the basis of some examples. 1
Doing Argumentation Theory in Modal Logic
, 2009
"... The present paper applies wellinvestigated modal logics to provide formal foundations to specific fragments of argumentation theory. This logicdriven analysis of argumentation allows: first, to systematize several results of argumentation theory reformulating them within suitable formal languages; ..."
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The present paper applies wellinvestigated modal logics to provide formal foundations to specific fragments of argumentation theory. This logicdriven analysis of argumentation allows: first, to systematize several results of argumentation theory reformulating them within suitable formal languages; second, to import several techniques (calculi, modelchecking, evaluation games, bisimulation games); third, to import results (eminently completeness of axiomatizations, and complexity of modelchecking) from modal logic to argumentation theory.
MSc in Logic
, 2008
"... we elaborate on logicbased automated reasoning techniques for abduction, driven by the principle of goaloriented reasoning. In the first part we develop two variants of a computational framework for abduction in propositional logic, based on regular connection tableaux and resolution with setofs ..."
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we elaborate on logicbased automated reasoning techniques for abduction, driven by the principle of goaloriented reasoning. In the first part we develop two variants of a computational framework for abduction in propositional logic, based on regular connection tableaux and resolution with setofsupport. The procedures are proven to be sound and complete calculi for finding consistent, minimal and relevant solutions to abductive problems. In the second part we adapt the framework to the Description Logic ALC. We obtain a procedure for solving ABox abduction problems (i.e. abductive problems whose main part of the input and every solution are specified by a set of ABox assertions), for which we prove the results of (plain) soundness and (minimality) completeness. Contents
Tool support for reasoning in display calculi
"... Abstract. We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calcu ..."
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Abstract. We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of metatools, that allows us to adapt the tool for a wide variety of user defined calculi. 1
Swap Logic
"... Abstract. We investigate dynamic modal operators that can change the model during evaluation. We define the logic SL by extending the basic modal language with the ♦ modality, which is a diamond operator that in addition has the ability to invert pairs of related elements in the domain while traver ..."
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Abstract. We investigate dynamic modal operators that can change the model during evaluation. We define the logic SL by extending the basic modal language with the ♦ modality, which is a diamond operator that in addition has the ability to invert pairs of related elements in the domain while traversing an edge of the accessibility relation. SL is very expressive: it fails to have the finite and the tree model property. We show that SL is equivalent to a fragment of firstorder logic by providing a satisfiability preserving translation. In addition, we provide an equivalence preserving translation from SL to the hybrid logicH(:, ↓). We also define a suitable notion of bisimulation for SL and investigate its expressive power, showing that it lies strictly between the basic modal logic and H(:, ↓). We finally show that its model checking problem is PSpacecomplete and its satisfiability problem is undecidable.
The Impact of Including Model Update Operators in Modal Logics
"... Abstract. In this paper we discuss ideas about dynamic modal logics. Modal logics are appropriate to describe properties of relational structures, and several operators have been already introduced to describe dynamic properties of such structures. However, we are interested in those operators whic ..."
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Abstract. In this paper we discuss ideas about dynamic modal logics. Modal logics are appropriate to describe properties of relational structures, and several operators have been already introduced to describe dynamic properties of such structures. However, we are interested in those operators which can modify models during the evaluation of a formula. First, we introduce different dynamic operators to clarify which of them are interesting for us. Then we focus on operators which modify the accessibility relation of relational models, and we show some expressivity results.