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10
Counting Objects
, 1995
"... We survey results on axiomatic completeness and complexity of formal languages for reasoning about finite quantities. These languages are interpreted on domains with and without structure. Expressions dealt with include 'at least n Xs are Ks, ' in the case of unstructured domains, and 'at leait n 'r ..."
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Cited by 20 (1 self)
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We survey results on axiomatic completeness and complexity of formal languages for reasoning about finite quantities. These languages are interpreted on domains with and without structure. Expressions dealt with include 'at least n Xs are Ks, ' in the case of unstructured domains, and 'at leait n 'related ' Xi are Y%, ' in the structured case. The results contained in this paper are brought together from generalized quantifier theory, modal logic, and knowledge representation, while a few new results are also included. A unifying approach is offered to the wide variety of formalisms available in the literature.
Hybridizing Concept Languages
 Annals of Mathematics and Artificial Intelligence
"... This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the wellknown correspondences between modal and description logics, two hybrid languages are dened. These languages are called `hybrid' because, as well as the familiar prop ..."
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Cited by 17 (8 self)
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This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the wellknown correspondences between modal and description logics, two hybrid languages are dened. These languages are called `hybrid' because, as well as the familiar propositional variables and modal operators, they also contain variables across individuals and a binder that binds these variables. As is shown, combining aspects of modal and rstorder logic in this manner allows the expressivity of concept languages to be boosted in a natural way, making it possible to dene number restrictions, collections of individuals, irreexivity of roles, and TBox and ABoxstatements. Subsequent addition of the universal modality allows the notion of subsumption to internalized, and enables the representation of queries to arbitrary rstorder knowledge bases. The paper notes themes shared by the hybrid and concept language literatures, and draws attention t...
Presuppositions and Information Updating
, 1995
"... Presupposition failures are errors occurring during the leftright processing of a computer program or natural language text. A general method for analysing such errors with dynamic logic is presented, based on the idea that sequential processing changes context dynamically and that this process o ..."
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Cited by 4 (1 self)
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Presupposition failures are errors occurring during the leftright processing of a computer program or natural language text. A general method for analysing such errors with dynamic logic is presented, based on the idea that sequential processing changes context dynamically and that this process of context change can be made the object of analysis in dynamic modal logic.
Relational Grammars for Knowledge Representation
, 1996
"... This paper aims to enhance the practical applicability of relational grammars, which have been devised for the semantic analysis of natural language. We focus on their application in knowledge representation. In particular, we address how the representation problem for klonebased knowledge rep ..."
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Cited by 4 (1 self)
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This paper aims to enhance the practical applicability of relational grammars, which have been devised for the semantic analysis of natural language. We focus on their application in knowledge representation. In particular, we address how the representation problem for klonebased knowledge representation systems can be automatically solved with the help of relational grammars. New rules are presented for natural language formulations, like has sons and has at least two sons, commonly arising in application domains. For accommodating the latter kind of sentences we introduce a new class of socalled (concrete) graded Peirce algebras. A graded Peirce algebra is a Peirce algebra endowed with a countable set of numerical quantifier operations.
doi:10.1111/j.17552567.2011.01119.x Everything is Knowable – How to Get to Know Whether a Proposition is Truetheo_1119 1..22
, 2012
"... Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known af ..."
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Cited by 2 (1 self)
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Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch’s and Moore’s results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we interpret ‘successful ’ as ‘known after its announcement ’ and ‘knowable ’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a proposition j that is not known after its announcement but there is another announcement after which j is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: �(Kj ⁄ K¬j). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting ‘knowable ’ as ‘known after an announcement’. Keywords: modal logic, knowability, Fitch’s paradox, dynamic epistemics, public announcements 1. Successful – the Historical Record
Describing the Approaches
, 1994
"... ing from the nature of the states involved, we can specify the change that an atomic program a effects by means of a two place transition relation R a on a set of states. This perspective gives rise to the study of socalled transition systems. The most general style of reasoning about programs and ..."
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ing from the nature of the states involved, we can specify the change that an atomic program a effects by means of a two place transition relation R a on a set of states. This perspective gives rise to the study of socalled transition systems. The most general style of reasoning about programs and transition system is found in propositional dynamic logics (Pratt [ Pratt, 1976 ] [ Pratt, 1980 ] , Harel [ Harel, 1984 ] ) and in algebras of processes (Hennessy [ Hennessy, 1988 ] ). Processes and transition systems are studied from the perspective of modal logic in Stirling [ Stirling, 1987 ] and Van Benthem and Bergstra [ Benthem and Bergstra, 1993 ] . Dynamic semantics can be put to use to stipulate relational denotations for propositions. In this perspective, a state of information is a set of possible worlds, and a program updates a state of information by removing the worlds incompatible with the new information. Thus, the semantics of language is defined in terms of its potential to...
Reasoning about Changing Information
, 1997
"... The purpose of these notes is twofold: (i) to give a reasonably selfcontained introduction to a particular approach to theory change, known as the Alchourr'onGardenforsMakinson (AGM) approach, and to discuss some of the alternatives, and extensions that have been proposed to it over the past few ..."
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The purpose of these notes is twofold: (i) to give a reasonably selfcontained introduction to a particular approach to theory change, known as the Alchourr'onGardenforsMakinson (AGM) approach, and to discuss some of the alternatives, and extensions that have been proposed to it over the past few years; (ii) to relate the AGM approach to other `informationoriented' branches of logic, including intuitionistic logic, nonmonotonic reasoning, verisimilitude, and modal and dynamic logic. Keywords: Theory change, knowledge representation, modal logic, dynamic logic. Computing Review Categories: F.4.0, F.4.1, I.2.3, I.2.4. 1 Introduction In these notes we study a number of approaches to theory change alias belief revision alias belief change alias theory revision. This enterprise is about coping with changing information, either because new facts have become known, or because the world has changed. If the newly obtained information is consistent with our old theory, there's no proble...
1 HOW LOGIC EMERGES FROM THE DYNAMICS OF INFORMATION
"... Abstract: It is often claimed that the symbolic approach to information processing is incompatible with connectionism and other associationist modes of representing information. I propose to throw new light on this debate by presenting two examples of how logic can be seen as emerging from an underl ..."
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Abstract: It is often claimed that the symbolic approach to information processing is incompatible with connectionism and other associationist modes of representing information. I propose to throw new light on this debate by presenting two examples of how logic can be seen as emerging from an underlying information dynamics. The first example shows how intuitionistic logic results very naturally from an abstract analysis of the dynamics of information. The second example establishes that the activities of a large class of neural networks may be interpreted, on the symbolic level, as nonmonotonic inferences. On the basis of these examples I argue that symbolic and nonsymbolic approaches to information can be described in terms of different perspectives on the same phenomenon. Thus, I find that Fodor and Pylyshyn’s claim that connectionist systems cannot be systematic and compositional is based on a misleading interpretation of representations in such systems.