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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.
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.
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).
Games, Actions, and Social Software
"... 2. Games as models for modal process logics 6 3. Preference structure and more realistic games 9 ..."
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2. Games as models for modal process logics 6 3. Preference structure and more realistic games 9
Keywords Description Logic · Abduction · Nonstandard Reasoning Services · Semantic Tableaux · Resolution
, 2010
"... Abstract Due to the growing popularity of Description Logicsbased knowledge representation systems, predominantly in the context of Semantic Web applications, there is a rising demand for tools offering nonstandard reasoning services. One particularly interesting form of reasoning, both from the u ..."
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Abstract Due to the growing popularity of Description Logicsbased knowledge representation systems, predominantly in the context of Semantic Web applications, there is a rising demand for tools offering nonstandard reasoning services. One particularly interesting form of reasoning, both from the user as well as the ontology engineering perspective, is abduction. In this paper we introduce two novel reasoning calculi for solving ABox abduction problems in the Description Logic ALC, i.e. problems of finding minimal sets of ABox axioms, which when added to the knowledge base enforce entailment of a requested set of assertions. The algorithms are based on regular connection tableaux and resolution with setofsupport and are proven to be sound and complete. We elaborate on a number of technical issues involved and discuss some practical aspects of reasoning with the methods.
Computation as Conversation
"... Against the backdrop of current research into 'logical dynamics ' of information, we discuss twoway connections between conversation and computation, leading to a broader perspective on both. 1 Information flow for children, and logical dynamics The Amsterdam Science Museum NEMO organizes ..."
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Against the backdrop of current research into 'logical dynamics ' of information, we discuss twoway connections between conversation and computation, leading to a broader perspective on both. 1 Information flow for children, and logical dynamics The Amsterdam Science Museum NEMO organizes regular Kids ' Lectures on Science. 1 Imagine 60 children aged aged around 8 sitting in a small amphitheatre – with parents present in the wings, but not allowed to speak. Last February, it was my pleasure to give one on Logic. While preparing for the event, I got more and more worried. How does one talk logic to such an audience, without boring or upsetting them? Was there anything in common between children that age and the abstractions that drive one's university career? How to even start? My first question was this: The Restaurant In a restaurant, your Father has ordered Fish, your Mother ordered Vegetarian, and you have Meat. Out of the kitchen comes some new person with the three plates. What will happen? The children got excited, many little hands were raised, and one said: &quot;He asks who has the Meat&quot;. &quot;Sure
In Praise of Strategies
, 2007
"... This note highlights one major theme in my lecture notes Logic in Games (van Benthem 1999 – 2002): the need for explicit logics that define agents ’ strategies, as the drivers of interaction in games. Our text outlines issues, recalls published results from the last few years, and raises new open p ..."
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This note highlights one major theme in my lecture notes Logic in Games (van Benthem 1999 – 2002): the need for explicit logics that define agents ’ strategies, as the drivers of interaction in games. Our text outlines issues, recalls published results from the last few years, and raises new open problems. Results are mainly quoted, and the mephasis is on new notions and open problems. For more details on the various topics discussed, see the relevant references. 1 Strategies as firstclass citizens Much of game theory is about the question whether strategic equilibria exist. But there are hardly any explicit languages for defining, comparing, or combining strategies as such – the way we have them for actions and plans, maybe the closest intuitive analogue to strategies. True, there are many current logics for describing game structure – but these tend to have existential quantifiers saying that “players have a strategy ” for achieving some purpose, while descriptions of these strategies themselves are not part of the logical language (cf. Parikh & Pauly 2003, van der Hoek, van Otterloo & Wooldridge 2005). Therefore, I consider strategies 'the unsung heroes of game theory ' and I want to show how the right
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
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