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A Unifying Action Calculus
- Artificial Intelligence
, 2010
"... Abstract McCarthy’s Situation Calculus is arguably the oldest special-purpose knowledge representa-tion 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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Cited by 14 (6 self)
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Abstract McCarthy’s Situation Calculus is arguably the oldest special-purpose knowledge representa-tion 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 co-existence of many different cal-culi 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 (well-defined 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, calculus-independent 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 on-tologies in description logics. It turns out that with existing accounts of modularity of ontologies we do not completely avoid unforeseen in-teractions between module components, and modules designed in those ways may be as comple ..."
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Cited by 9 (7 self)
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Abstract. In this paper we address the principle of modularity of on-tologies in description logics. It turns out that with existing accounts of modularity of ontologies we do not completely avoid unforeseen in-teractions between module components, and modules designed in those ways may be as complex as whole theories. We here give a more fine-grained 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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Cited by 6 (5 self)
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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 Kripke-models. 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 AGM-like 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 normal-ity of the premise. In this paper we are interested in an-other 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 normal-ity of the premise. In this paper we are interested in an-other aspect of defeasibility, namely that of defeasible modes of reasoning. We do this by adopting a preferen-tial 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 preferen-tial versions of the traditional notions of knowledge, be-liefs, 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 for-malisms.
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 pres-ence of some notion of ‘conditional ’ that fails monotonicity. Research on nonmonotonic logics is therefore largely con-cerned with the defeasibility of argument forms and the as-sociated 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 pres-ence of some notion of ‘conditional ’ that fails monotonicity. Research on nonmonotonic logics is therefore largely con-cerned with the defeasibility of argument forms and the as-sociated normality (or abnormality) of its constituents. In contrast, defeasible modes of inference aim to formalize the defeasible aspects of modal notions such as actions, obli-gations and knowledge. In this work we enrich the stan-dard 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 modali-ties. We also propose a tableau calculus which is sound and complete with respect to our preferential semantics. Keywords Knowledge representation and reasoning; modal logic; pref-erential 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 proposi-tional 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 proposi-tional 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 KLM-style preferential reasoning. This allows us to show that KLM-style 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 exist-ing link between propositional rational consequence and belief revision, we show that the same correspondence holds in the case of rational con-sequence 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 descrip-tions (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 incor-porated solution to the frame ..."
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Cited by 2 (2 self)
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In this work we address the problem of elaborating domain descrip-tions (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 incor-porated 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 non-modular 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 Kripke-models. 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
