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A Unifying Action Calculus
 Artificial Intelligence
, 2010
"... Abstract McCarthy’s Situation Calculus is arguably the oldest specialpurpose knowledge representation formalism, designed to axiomatize knowledge of actions and their effects. Four decades of research in this area has led to a variety of alternative formalisms: While some approaches can be conside ..."
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Abstract McCarthy’s Situation Calculus is arguably the oldest specialpurpose knowledge representation formalism, designed to axiomatize knowledge of actions and their effects. Four decades of research in this area has led to a variety of alternative formalisms: While some approaches can be considered instances or extensions of the classical Situation Calculus, like Reiter’s successor state axioms or the Fluent Calculus, there also exist special planning languages like ADL and approaches based on a linear (rather than branching) time structure like the Event Calculus. The coexistence of many different calculi has two main disadvantages: The formal relations among them is a largely open issue, and a lot of today’s research concerns the transfer of specific results obtained for one approach to another one. In this paper, we present a unifying action calculus, of which we show that it encompasses (welldefined classes of) all of the aforementioned formalisms. Our calculus not only facilitates comparisons and translations between specific approaches, it also allows to solve interesting problems for various calculi at once. We exemplify this by providing a general, calculusindependent solution to a problem of practical relevance: the modularity of domain axiomatizations. 1
A modularity approach for a fragment of ALC
 In
, 2006
"... Abstract. In this paper we address the principle of modularity of ontologies in description logics. It turns out that with existing accounts of modularity of ontologies we do not completely avoid unforeseen interactions between module components, and modules designed in those ways may be as comple ..."
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Abstract. In this paper we address the principle of modularity of ontologies in description logics. It turns out that with existing accounts of modularity of ontologies we do not completely avoid unforeseen interactions between module components, and modules designed in those ways may be as complex as whole theories. We here give a more finegrained paradigm for modularizing descriptions. We propose algorithms that check whether a given terminology is modular and that also help the designer making it modular, if needed. Completeness, correctness and termination results are demonstrated for a fragment of ALC. We also present the properties that ontologies that are modular in our sense satisfy w.r.t. reasoning services.
On Action Theory Change
"... As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus knowledge engineers need revision methods to help in accommoda ..."
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As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus knowledge engineers need revision methods to help in accommodating new incoming information about the behavior of actions in an adequate manner. The present work is about changing action domain descriptions in multimodal logic. Its contribution is threefold: first we revisit the semantics of action theory contraction proposed in previous work, giving more robust operators that express minimal change based on a notion of distance between Kripkemodels. Second we give algorithms for syntactical action theory contraction and establish their correctness with respect to our semantics for those action theories that satisfy a principle of modularity investigated in previous work. Since modularity can be ensured for every action theory and, as we show here, needs to be computed at most once during the evolution of a domain description, it does not represent a limitation at all to the method here studied. Finally we state AGMlike postulates for action theory contraction and assess the behavior of our operators with respect to them. Moreover, we also address the revision counterpart of action theory change, showing that it benefits from our semantics for contraction. 1.
I.: Defeasible modes of inference: A preferential perspective
 In: Proceedings of the 14th International Workshop on Nonmonotonic Reasoning (NMR) (2012
"... Historically, approaches to defeasible reasoning have been concerned mostly with one aspect of defeasibility, viz. that of arguments, in which the focus is on normality of the premise. In this paper we are interested in another aspect of defeasibility, namely that of defeasible modes of reasoning. ..."
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Cited by 5 (4 self)
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Historically, approaches to defeasible reasoning have been concerned mostly with one aspect of defeasibility, viz. that of arguments, in which the focus is on normality of the premise. In this paper we are interested in another aspect of defeasibility, namely that of defeasible modes of reasoning. We do this by adopting a preferential modal semantics that we defined in previous work and which allows us to refer to the relative normality of accessible worlds. This leads us to define preferential versions of the traditional notions of knowledge, beliefs, obligations and actions, to name a few, as studied in modal logics. The resulting preferential modal logics make it possible to capture, and reason with, aspects of defeasibility heretofore beyond the reach of modal formalisms.
I.: Defeasible modalities
 In: Proceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge (TARK
, 2013
"... Nonmonotonic logics are usually characterized by the presence of some notion of ‘conditional ’ that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the associated normality (or abnormality) of its constituents. In con ..."
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Cited by 5 (2 self)
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Nonmonotonic logics are usually characterized by the presence of some notion of ‘conditional ’ that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the associated normality (or abnormality) of its constituents. In contrast, defeasible modes of inference aim to formalize the defeasible aspects of modal notions such as actions, obligations and knowledge. In this work we enrich the standard possible worlds semantics with a preference ordering on worlds in Kripke models. The resulting family of modal logics allow for the elegant expression of defeasible modalities. We also propose a tableau calculus which is sound and complete with respect to our preferential semantics. Keywords Knowledge representation and reasoning; modal logic; preferential semantics; defeasible modes of inference
I.: A propositional typicality logic for extending rational consequence
 Trends in Belief Revision and Argumentation Dynamics, Studies in Logic – Logic and Cognitive Systems
, 2013
"... abstract. We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical propositional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a given formula holds. The semant ..."
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Cited by 3 (2 self)
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abstract. We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical propositional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a given formula holds. The semantics is in terms of ranked models as studied in KLMstyle preferential reasoning. This allows us to show that KLMstyle rational consequence relations can be embedded in our logic. Moreover we show that we can define consequence relations on the language of PTL itself, thereby moving beyond the propositional setting. Building on the existing link between propositional rational consequence and belief revision, we show that the same correspondence holds in the case of rational consequence and belief revision defined on the language of PTL. Finally we also investigate different notions of entailment for PTL and propose two appropriate candidates.
Elaborating domain descriptions (preliminary report
, 2006
"... In this work we address the problem of elaborating domain descriptions (alias action theories), in particular those that are expressed in dynamic logic. We dene a general method based on contraction of formulas in a version of propositional dynamic logic with an incorporated solution to the frame ..."
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In this work we address the problem of elaborating domain descriptions (alias action theories), in particular those that are expressed in dynamic logic. We dene a general method based on contraction of formulas in a version of propositional dynamic logic with an incorporated solution to the frame problem. We present the semantics of our theory change and dene syntactical operators for contracting a domain description. We establish soundness and completeness of the operators w.r.t. the semantics for descriptions that satisfy a principle of modularity that we have proposed elsewhere. We also investigate an example of changing nonmodular domain descriptions.
2.2 Essential Atoms.......................... 11
, 811
"... Like any other logical theory, domain descriptions in reasoning about actions may evolve, and thus need revision methods to adequately accommodate new information about the behavior of actions. The present work is about changing action domain descriptions in propositional dynamic logic. Its contribu ..."
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Like any other logical theory, domain descriptions in reasoning about actions may evolve, and thus need revision methods to adequately accommodate new information about the behavior of actions. The present work is about changing action domain descriptions in propositional dynamic logic. Its contribution is threefold: first we revisit the semantics of action theory contraction that has been done in previous work, giving more robust operators that express minimal change based on a notion of distance between Kripkemodels. Second we give algorithms for syntactical action theory contraction and establish their correctness w.r.t. our semantics. Finally we state postulates for action theory contraction and assess the behavior of our operators w.r.t. them. Moreover, we also address the revision counterpart of action theory change, showing that it benefits from our semantics for