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13
I.: Semantic foundation for preferential description logics
- In: Proc. of Australasian AI Conference
, 2011
"... Abstract. Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching descrip-tion logics with non-monotonic reasoning capabilities, especially prefer-ential reasoning as developed by Lehmann and colleagues in the 90’s, would therefor ..."
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Abstract. Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching descrip-tion logics with non-monotonic reasoning capabilities, especially prefer-ential reasoning as developed by Lehmann and colleagues in the 90’s, would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in description logics. In this paper we fill this gap by providing a natu-ral and intuitive semantics for defeasible subsumption in the description logic ALC. Our semantics replaces the propositional valuations used in the models of Lehmann et al. with structures we refer to as concept mod-els. We present representation results for the description logic ALC for both preferential and rational consequence relations. We argue that our semantics paves the way for extending preferential and rational conse-quence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of first-order relational structures. 1
PTL: A propositional typicality logic
, 2012
"... Abstract. We introduce Propositional Typicality Logic (PTL), a logic for rea-soning 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 nor-mal) situations in which a formula holds. The semantics i ..."
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Abstract. We introduce Propositional Typicality Logic (PTL), a logic for rea-soning 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 nor-mal) situations in which a formula holds. The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that 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 for rational consequence and belief revision on PTL. We investigate entailment for PTL, and propose two appropriate notions thereof.
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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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
Nonmonotonic Reasoning in Description Logics: Rational Closure for the ABox
"... Abstract. The introduction of defeasible reasoning in description logics has been a main research topic in the field in the last years. Despite the fact that various interesting formalizations of nonmonotonic reasoning for the TBox have been proposed, the application of such a kind of reasoning also ..."
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Abstract. The introduction of defeasible reasoning in description logics has been a main research topic in the field in the last years. Despite the fact that various interesting formalizations of nonmonotonic reasoning for the TBox have been proposed, the application of such a kind of reasoning also to ABoxes is more problematic. In what follows we are going to present the adaptation for the ABox of a classical nonmonotonic form of reasoning, namely Lehmann and Magidor’s Rational Closure. We present both a procedural and a semantical characterization, and we conclude the paper with a comparison between our and other analogous proposals. 1
Preferential Role Restrictions
"... Abstract. We extend ALC with preferential role restrictions as concept constructors, and argue that preferential universal restriction represents a defeasible version of standard universal restriction. The resulting DL is more expressive without adding to the complexity of TBox reasoning. We present ..."
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Abstract. We extend ALC with preferential role restrictions as concept constructors, and argue that preferential universal restriction represents a defeasible version of standard universal restriction. The resulting DL is more expressive without adding to the complexity of TBox reasoning. We present a tableau system to compute TBox entailment, show that this notion of entailment is not sufficient when adding ABoxes, and refine entailment to deal adequately with ABox reasoning. 1
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.
A Protégé Plug-in for Defeasible Reasoning
"... Abstract. We discuss two approaches for defeasible reasoning in Description Logics that allow for the statement of defeasible subsumptions of the form “α subsumed by β usually holds”. These approaches are known as prototypical reasoning and presumptive reasoning and are both rooted in the notion of ..."
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Abstract. We discuss two approaches for defeasible reasoning in Description Logics that allow for the statement of defeasible subsumptions of the form “α subsumed by β usually holds”. These approaches are known as prototypical reasoning and presumptive reasoning and are both rooted in the notion of Rational Closure developed by Lehmann and Magidor for the propositional case. Here we recast their definitions in a defeasible DL context and define algorithms for prototypical and presumptive reasoning in defeasible DL knowledge bases. In particular, we present a plug-in for the Protégé ontology editor which implements these algorithms for OWL ontologies. The plug-in is called RaMP and allows the modeller to indicate defeasible information in OWL ontologies and check entailment of defeasible subsumptions from defeasible knowledge bases. 1
Normal modal preferential consequence
- Proc. Australasian Joint Conference on Artificial Intelligence, number 7691 in LNAI
, 2012
"... Abstract. One of the most successful approaches to the formalization of commonsense reasoning is the work by Lehmann and colleagues, known as the KLM approach, in which defeasible consequence relations with a preferential semantics are studied. In spite of its success, KLM is limited to propositiona ..."
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Abstract. One of the most successful approaches to the formalization of commonsense reasoning is the work by Lehmann and colleagues, known as the KLM approach, in which defeasible consequence relations with a preferential semantics are studied. In spite of its success, KLM is limited to propositional logic. In recent work we provided the semantic founda-tion for extending defeasible consequence relations to modal logics and description logics. In this paper we continue that line of investigation by going beyond the basic (propositional) KLM postulates, thereby making use of the additional expressivity provided by modal logic. In particular, we show that the additional constraints we impose on the preferential se-mantics ensure that the rule of necessitation holds for the corresponding consequence relations, as one would expect it to. We present a represen-tation result for this tightened framework, and investigate appropriate notions of entailment in this context — normal entailment, and a rational version thereof.
A defeasible reasoning approach for description logic ontologies
- In Proceedings of the South African Institute for Computer Scientists and Information Technologists Conference
, 2012
"... Classical reasoning for logic-based KR (Knowledge Represen-tation) systems is in general, monotonic. That is, there is an assumption in these systems that there is complete information about a domain. This means that they generally cannot deal with any new information arising which contradicts with ..."
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Classical reasoning for logic-based KR (Knowledge Represen-tation) systems is in general, monotonic. That is, there is an assumption in these systems that there is complete information about a domain. This means that they generally cannot deal with any new information arising which contradicts with the current information. This is not an appropriate model for reasoning in many applications. Therefore, alternative non-monotonic sys-tems have been investigated which can reason under uncertainty or with incomplete information. Defeasible reasoning is one par-ticular model for implementing non-monotonic reasoning. It is concerned with representing and reasoning with defeasible (non-strict) facts about a domain. The defeasible counterpart of the strict fact: “All birds fly ” is the defeasible fact: “Most birds fly ” (or the alternative phrasing “Birds usually fly”). We discuss
