Results 1  10
of
17
Plausibility Measures and Default Reasoning
 Journal of the ACM
, 1996
"... this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. W ..."
Abstract

Cited by 90 (14 self)
 Add to MetaCart
(Show Context)
this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:
Nonmonotonic Logics and Semantics
 Journal of Logic and Computation
, 2001
"... Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas i a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may be deduced from a set A of formulas i a holds in all of th ..."
Abstract

Cited by 31 (4 self)
 Add to MetaCart
(Show Context)
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas i a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may be deduced from a set A of formulas i a holds in all of the preferred models in which all the elements of A hold. Shoham proposed that the notion of preferred models be de ned by a partial ordering on the models of the underlying language. A more general semantics is described in this paper, based on a set of natural properties of choice functions. This semantics is here shown to be equivalent to a semantics based on comparing the relative importance of sets of models, by what amounts to a qualitative probability measure. The consequence operations de ned by the equivalent semantics are then characterized by a weakening of Tarski's properties in which the monotonicity requirement is replaced by three weaker conditions. Classical propositional connectives are characterized by natural introductionelimination rules in a nonmonotonic setting. Even in the nonmonotonic setting, one obtains classical propositional logic, thus showing that monotonicity is not required to justify classical propositional connectives.
Modeling Beliefs In Dynamic Systems
, 1997
"... tions beliefs. We say that an agent believes ' if she acts as though ' is true. As time passes and new evidence is observed, changes in an agent's defeasible assumptions lead to changes in her beliefs. Thus, the question of belief changethat is, how beliefs change over timeis a ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
tions beliefs. We say that an agent believes ' if she acts as though ' is true. As time passes and new evidence is observed, changes in an agent's defeasible assumptions lead to changes in her beliefs. Thus, the question of belief changethat is, how beliefs change over timeis a central one for understanding systems that can make and modify defeasible assumptions. In this dissertation, we propose a new approach to the question of belief change. This approach is based on developing a semantics for beliefs. This semantics is embedded in a framework that models agents' knowledge (or information) as well as their beliefs, and how these change in time. We argue, and demonstrate by examples, that this framework can naturally model any dynamic system (e.g., agents and their environment). Moreover, the framework allows us to consider what the properties of wellbehaved belief change should be. As we show, such a framework can g
A Multiple Worlds Semantics to a Paraconsistent Nonmonotonic Logic
"... Semantics has been many times a problem in connection to both nonmonotonic and paraconsistent logics. In previous works, a system of logics called IDL & LEI was developed to formalize practical reasoning, i.e., reasoning under incomplete knowledge. This system combines the features of nonmonoton ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Semantics has been many times a problem in connection to both nonmonotonic and paraconsistent logics. In previous works, a system of logics called IDL & LEI was developed to formalize practical reasoning, i.e., reasoning under incomplete knowledge. This system combines the features of nonmonotonicity to model inferences on the basis of partial evidence, with paraconsistency to deal with the inconsistencies introduced by extended inferences. The aim of this paper is to present a semantics that is, as much as possible, uniform with respect to both deductive and nonmonotonic part of this system. This semantics is presented in a possible worlds style and is intended to reect the basic intuitions assumed in designing IDL & LEI. A possible worlds semantics to the paraconsistent logic LEI is rst given and it is extended to encompass the nonmonotonic features formalized by the logic IDL. The resulting semantics is shown to be sound and complete with respect to the whole IDL & LEI system.
Defeasible inheritance systems and reactive diagrams ∗
, 2008
"... Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y (read x is a y) and x ̸ → y (read as x is not a y). Given a diagram D, one can ask the formal question of “is there a valid (winning) path between node x and node y? ” Depending on the existence of a ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y (read x is a y) and x ̸ → y (read as x is not a y). Given a diagram D, one can ask the formal question of “is there a valid (winning) path between node x and node y? ” Depending on the existence of a valid path we can answer the question “x is a y ′ ′ or ”x is not a y ′ ′. The answer to the above question is determined through a complex inductive algorithm on paths between arbitrary pairs of points in the graph. This paper aims to simplify and interpret such diagrams and their algorithms. We approach the area on two fronts. (1) Suggest reactive arrows to simplify the algorithms for the winning paths. (2) We give a conceptual analysis of (defeasible or nonmonotonic) inheritance diagrams, and compare our analysis to the “small ” and “big sets ” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information,
A modal view on abstract learning and reasoning
"... Abstract. We present here a view on abstraction based on the relation between sentences in a partially ordered language L and truth values of these sentences on a set of instances W. In Formal Concept Analysis, this relation is materialized as a lattice denoted as G that relates L and the powerset P ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We present here a view on abstraction based on the relation between sentences in a partially ordered language L and truth values of these sentences on a set of instances W. In Formal Concept Analysis, this relation is materialized as a lattice denoted as G that relates L and the powerset P(W)). We show here that projections on a lattice (here either L or the powerset P(W)) that are known to ensure structurepreserving reductions of G, are equivalent to abstractions, defined here as sets of subsets closed under union (regarding P(W)) or under minimal specialization (regarding L) and order them in a lattice of abstractions. We then discuss specifically abstractions A of P(W) and discuss the properties, of abstract implications. We then exhibit the class of (non normal) monotonic modal logics the semantic basis of which relies on such abstractions, and discuss how reasoning may be performed at variable abstraction levels. 1
Abstract Concept Lattices
"... Abstract. We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerset of a set of instances O. Such a relation is materialized as an extensionintension lattice, namely a concept lattice when L is the powerset of ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerset of a set of instances O. Such a relation is materialized as an extensionintension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extensionintension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties. 1
AN ANALYSIS OF DEFEASIBLE INHERITANCE SYSTEMS
, 2007
"... We give a conceptual analysis of (defeasible or nonmonotonic) inheritance diagrams, and compare our analysis to the ”small/big sets ” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as inf ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We give a conceptual analysis of (defeasible or nonmonotonic) inheritance diagrams, and compare our analysis to the ”small/big sets ” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as information channels and comparisons of truth values. This results in an upward chaining, split validity, offpath preclusion inheritance formalism. We show that the small/big sets of preferential reasoning have to be relativized if we want them to conform to inheritance theory, resulting in a more cautious approach, perhaps closer to actual human reasoning. Finally, we interpret inheritance diagrams as theories of prototypical reasoning, based on two distances: set difference, and information difference. We will also see that some of the major distinctions between inheritance formalisms are consequences of deeper and more general problems of treating conflicting
unknown title
"... In this paper we investigate nonmonotonic ‘modes of inference’. Our approach uses modal (conditional) logic to establish a uniform framework in which to study nonmonotonic consequence. We consider a particular mode of inference which employs a majoritybased account of default reasoning—one which di ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper we investigate nonmonotonic ‘modes of inference’. Our approach uses modal (conditional) logic to establish a uniform framework in which to study nonmonotonic consequence. We consider a particular mode of inference which employs a majoritybased account of default reasoning—one which differs from the more familiar preferential accounts—and show how modal logic supplies a framework which facilitates analysis of, and comparison with more traditional formulations of nonmonotonic consequence.
DOI: 10.1007/9783642205149_18 Abstract Concept Lattices
, 2011
"... Abstract. We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerset of a set of instances O. Such a relation is materialized as an extensionintension lattice, namely a concept lattice when L is the powerset of ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerset of a set of instances O. Such a relation is materialized as an extensionintension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extensionintension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties. 1