Results 1 -
5 of
5
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 ..."
Abstract
-
Cited by 7 (6 self)
- Add to MetaCart
(Show Context)
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 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 ..."
Abstract
-
Cited by 5 (2 self)
- Add to MetaCart
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 ..."
Abstract
-
Cited by 3 (2 self)
- Add to MetaCart
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.
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 ..."
Abstract
-
Cited by 2 (2 self)
- Add to MetaCart
(Show Context)
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.
Towards a Logic of Dilation
"... Abstract. We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a seman-tic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, a ..."
Abstract
- Add to MetaCart
(Show Context)
Abstract. We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a seman-tic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, and a generalized no-tion of forgetting in propositional logic on the other hand. We place our work in the context of existing theories of approximation spaces and forgetting, and show that neighbourhoods obtained by combining collective and selective dilation pro-vide a suitable semantic framework within which to reason computationally with uncertainty in a classical setting.
