A representation methodology for knowledge allowing multiple interpretations is described. It is based on the following conception of legal knowledge and its open texture. Since indeterminate, legal knowledge must be adapted to fit the circumstances of the cases to which it is applied. Whether a certain adaptation is lawful or not is measured by metaknowledge. But as this too is indeterminate, its adaptation to the case must be measured by metametaknowledge, etc. This hierarchical model of law (...) is quite well-established and may serve well as a basis for a legal knowledge system. To account for the indeterminacy of law such a system should support the construction of different arguments for and against various interpretations of legal sources. However, automatizing this reasoning fully is unsound since it would imply a restriction to arguments defending interpretations anticipated at programming time. Therefore, the system must be interactive and the user''s knowledge be furnished in a principled way. Contrary to the widespread opinion that classical logic is inadequate for representing open-textured knowledge, the framework outlined herein is given a formalization in first order logic. (shrink)

Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection (...) of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99. (shrink)

Machine learning (ML) techniques have become pervasive across a range of different applications, and are now widely used in areas as disparate as recidivism prediction, consumer credit-risk analysis, and insurance pricing. Likewise, in the physical world, ML models are critical components in autonomous agents such as robotic surgeons and self-driving cars. Among the many ethical dimensions that arise in the use of ML technology in such applications, analyzing morally permissible actions is both immediate and profound. For example, there is the (...) potential for learned algorithms to become biased against certain groups. More generally, in so much that the decisions of ML models impact society, both virtually (e.g., denying a loan) and physically (e.g., driving into a pedestrian), notions of accountability, blame and responsibility need to be carefully considered. In this article, we advocate for a two-pronged approach ethical decision-making enabled using rich models of autonomous agency: on the one hand, we need to draw on philosophical notions of such as beliefs, causes, effects and intentions, and look to formalise them, as attempted by the knowledge representation community, but on the other, from a computational perspective, such theories need to also address the problems of tractable reasoning and (probabilistic) knowledge acquisition. As a concrete instance of this tradeoff, we report on a few preliminary results that apply (propositional) tractable probabilistic models to problems in fair ML and automated reasoning of moral principles. Such models are compilation targets for certain types of knowledge representation languages, and can effectively reason in service some computational tasks. They can also be learned from data. Concretely, current evidence suggests that they are attractive structures for jointly addressing three fundamental challenges: reasoning about possible worlds + tractable computation + knowledge acquisition. Thus, these seems like a good starting point for modelling reasoning robots as part of the larger ecosystem where accountability and responsibility is understood more broadly. (shrink)

Knowledge on regulatory relations, in for example regulatory pathways in biology, is used widely in experiment design by biomedical researchers and in systems biology. The knowledge has typically either been represented through simple graphs or through very expressive differential equation simulations of smaller sections of a pathway. As an alternative, in this work we suggest a knowledge representation of the most basic relations in regulatory processes regulates, positively regulates and negatively regulates in logics based on a (...) semantic analysis. We discuss the usage of these relations in biology and in artificial intelligence for hypothesis development in drug discovery. (shrink)

This article provides an overview of the subfield of Artificial Intelligence known as “Knowledge Representation and Reasoning.” This field uses the techniques of philosophical logic, but aims at providing a theoretical basis for the management of declarative information in automated reasoning systems. Three topics are singled out here for attention: planning and reasoning about actions, description logics, and nonmonotonic logics.

Knowledge representation, which lies at the core of artificial intelligence, is concerned with encoding knowledge on computers to enable systems to reason automatically. The aims are to help readers make their computer smarter, handle qualitative and uncertain information, and improve computational tractability.

Two different but closely related issues in current cognitive science will be considered in this essay. One is the controversial and extensively discussed question of how connectionist and symbolic representations of knowledge are related to each other. The other concerns the notion of connectionist learning and its relevance for the understanding of the distinction between propositional and nonpropositional knowledge. More specifically, I shall give an overview of a result in Rantala and Vadén (1994) establishing a limiting case correspondence (...) between symbolic and connectionist representations and, on the other hand, study the problem, preliminarily investigated in Rantala (1998), of how propositional knowledge may arise from nonpropositional knowledge. I shall also try to point out that on some more or less plausible assumptions, often made by cognitive scientists, these results may have some significance when we try to comprehend the nature of human knowledge representation. Some of these assumptions are rather hypothethical and debatable for the time being and they will become justified in the future only if there will be more progress in the empirical and theoretical research on the brain and on artificial networks. The assumptions concern, besides some questions of the behavior of neural networks, such things as the relevance of pattern recognition for modelling human cognition, in particular, knowledge acquisition, and the relation between emergence and reduction. (shrink)

in Handbook of Knowledge representation, Elsevier, 2008.

Contents: Foreword. Wolfgang BALZER and C. ULISES MOULINES: Introduction. José A. DÍEZ CALZADA: Structuralist Analysis of Theories of Fundamental Measurement. Adolfo GARCÍA DE LA SIENRA and Pedro REYES: The Theory of Finite Games in Extensive Form. Hans Joachim BURSCHEID und Horst STRUVE: The Theory of Stochastic Fairness - its Historical Development, Formulation and Justification. Wolfgang BALZER and Richard MATTESSICH: Formalizing the Basis of Accounting. Werner DIEDERICH: A Reconstruction of Marxian Economics. Bert HAMMINGA and Wolfgang BALZER: The Basic Structure of Neoclassical (...) General Equilibrium Theory. Klaus MANHART: Balance Theories: Two Reconstructions and the Problem of Intended Applications. Rainer WESTERMANN: Festinger's Theory of Cognitive Dissonance: A Structuralist Theory-Net. Rainer REISENZEIN: Wundt's Three-Dimensional Theory of Emotion. Pablo LORENZANO: Classical Genetics and the Theory-Net of Genetics. Hinne HETTEMA and Theo A.F. KUIPERS: The Formalisation of the Periodic Table. C. ULISES MOULINES: The Basic Core of Simple Equilibrium Thermodynamics. Thomas BARTELBORTH: An Axiomatization of Classical Electrodynamics. Author's Index. Subject Index. (shrink)

The information in the working environment of industrial Internet is characterized by diversity, semantics, hierarchy, and relevance. However, the existing representation methods of environmental information mostly emphasize the concepts and relationships in the environment and have an insufficient understanding of the items and relationships at the instance level. There are also some problems such as low visualization of knowledge representation, poor human-machine interaction ability, insufficient knowledge reasoning ability, and slow knowledge search speed, which cannot meet (...) the needs of intelligent and personalized service. Based on this, this paper designs a cognitive information representation model based on a knowledge graph, which combines the perceptual information of industrial robot ontology with semantic description information such as functional attributes obtained from the Internet to form a structured and logically reasoned cognitive knowledge graph including perception layer and cognition layer. Aiming at the problem that the data sources of the knowledge base for constructing the cognitive knowledge graph are wide and heterogeneous, and there are entity semantic differences and knowledge system differences among different data sources, a multimodal entity semantic fusion model based on vector features and a system fusion framework based on HowNet are designed, and the environment description information such as object semantics, attributes, relations, spatial location, and context acquired by industrial robots and their own state information are unified and standardized. The automatic representation of robot perceived information is realized, and the universality, systematicness, and intuition of robot cognitive information representation are enhanced, so that the cognition reasoning ability and knowledge retrieval efficiency of robots in the industrial Internet environment can be effectively improved. (shrink)

An introduction to the various logics of truth and modality as part of a foundation for the construction of theories of knowledge representation. The book reviews various semantic theories and employs them as the basis for the development of logics of truth and modality.

Although the connectionist approach has lead to elegant solutions to a number of problems in cognitive science and artificial intelligence, its suitability for dealing with problems in knowledge representation and inference has often been questioned. This paper partly answers this criticism by demonstrating that effective solutions to certain problems in knowledge representation and limited inference can be found by adopting a connectionist approach. The paper presents a connectionist realization of semantic networks, that is, it describes how (...) knowledge about concepts, their properties, and the hierarchical relationship between them may be encoded as an interpreter‐free massively parallel network of simple processing elements that can solve an interesting class of inheritance and recognition problems extremely fast—in time proportional to the depth of the conceptual hierarchy. The connectionist realization is based on an evidential formulation that leads to principled solutions to the problems of exceptions and conflicting multiple inheritance situations during inheritance, and the best‐match or partial‐match computation during recognition. The paper also identifies constraints that must be satisfied by the conceptual structure in order to arrive at an efficient parallel realization. (shrink)

. The current literature in the Artificial Intelligence and Law field reveals uncertainty concerning the potential role of deontic logic in legal knowledge representation. For instance, the Logic Programming Group at Imperial College has shown that a good deal can be achieved in this area in the absence of explicit representation of the deontic notions. This paper argues that some rather ordinary parts of the law contain structures which, if they are to be represented in logic, will (...) call for use of a reasonably sophisticated deontic logic. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels (...) of abstraction. Indeed, it is basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

Several approaches to implementing symbol-like representations in neurally plausible models have been proposed. These approaches include binding through synchrony, “mesh” binding, and conjunctive binding. Recent theoretical work has suggested that most of these methods will not scale well, that is, that they cannot encode structured representations using any of the tens of thousands of terms in the adult lexicon without making implausible resource assumptions. Here, we empirically demonstrate that the biologically plausible structured representations employed in the Semantic Pointer Architecture approach (...) to modeling cognition do scale appropriately. Specifically, we construct a spiking neural network of about 2.5 million neurons that employs semantic pointers to successfully encode and decode the main lexical relations in WordNet, which has over 100,000 terms. In addition, we show that the same representations can be employed to construct recursively structured sentences consisting of arbitrary WordNet concepts, while preserving the original lexical structure. We argue that these results suggest that semantic pointers are uniquely well-suited to providing a biologically plausible account of the structured representations that underwrite human cognition. (shrink)

This research employs Description Logics in order to focus on logical description and analysis of the phenomenon of ‘concept understanding’. The article will deal with a formal-semantic model for figuring out the underlying logical assumptions of ‘concept understanding’ in knowledge representation systems. In other words, it attempts to describe a theoretical model for concept understanding and to reflect the phenomenon of ‘concept understanding’ in terminological knowledge representation systems. Finally, it will design an ontology that schemes the (...) structure of concept understanding based on the proposed semantic model. (shrink)

Contents: Foreword. Wolfgang BALZER and C. ULISES MOULINES: Introduction. José A. DÍEZ CALZADA: Structuralist Analysis of Theories of Fundamental Measurement. Adolfo GARCÍA DE LA SIENRA and Pedro REYES: The Theory of Finite Games in Extensive Form. Hans Joachim BURSCHEID und Horst STRUVE: The Theory of Stochastic Fairness - its Historical Development, Formulation and Justification. Wolfgang BALZER and Richard MATTESSICH: Formalizing the Basis of Accounting. Werner DIEDERICH: A Reconstruction of Marxian Economics. Bert HAMMINGA and Wolfgang BALZER: The Basic Structure of Neoclassical (...) General Equilibrium Theory. Klaus MANHART: Balance Theories: Two Reconstructions and the Problem of Intended Applications. Rainer WESTERMANN: Festinger's Theory of Cognitive Dissonance: A Structuralist Theory-Net. Rainer REISENZEIN: Wundt's Three-Dimensional Theory of Emotion. Pablo LORENZANO: Classical Genetics and the Theory-Net of Genetics. Hinne HETTEMA and Theo A.F. KUIPERS: The Formalisation of the Periodic Table. C. ULISES MOULINES: The Basic Core of Simple Equilibrium Thermodynamics. Thomas BARTELBORTH: An Axiomatization of Classical Electrodynamics. Author's Index. Subject Index. (shrink)

The book contains a collection of eight survey papers written by some of the best researchers in foundations of knowledge representation and reasoning. It covers topics like theories of uncertainty, nonmonotonic and causal reasoning, logic programming, abduction, inductive logic programming, description logics, complexity in Artificial Intelligence, and model-based diagnosis. It thus provides an up-to-date coverage of recent approaches to some of the most challenging problems underlying knowledge representation and Artificial Intelligence in general.

ABSTRACT This is a continuing attempt in a series of papers [KM 93, Mur 93, Mur 96] to show how computer-represented knowledge can be arranged as elements of an effectively represented semantic (or algebraic) domain in the sense of [GS 90]. We present a direct deductive description of the domain, which was defined semantically in [KM 93], via the Scott's notion of information system. Also, the internal structure of the continuous ampliative operations coordinated with the domain's effective basis is (...) established. Though we always remain in the paradigm of the toleration of contradictory information described in [Bel 75, Bel 76], the approach in question could be extended to include domains for consistency knowledge bases. (shrink)

It is almost universally acknowledged that first-order logic (FOL), with its clean, well-understood syntax and semantics, allows for the clear expression of philosophical arguments and ideas. Indeed, an argument or philosophical theory rendered in FOL is perhaps the cleanest example there is of “representing philosophy”. A number of prominent syntactic and semantic properties of FOL reflect metaphysical presuppositions that stem from its Fregean origins, particularly the idea of an inviolable divide between concept and object. These presuppositions, taken at face value, (...) reflect a significant metaphysical viewpoint, one that can in fact hinder or prejudice the representation of philosophical ideas and arguments. Philosophers have of course noticed this and have, accordingly, sought to alter or extend traditional FOL in novel ways to reflect a more flexible and egalitarian metaphysical standpoint. The purpose of this paper, however, is to document and discuss how similar “adaptations” to FOL—culminating in a standardized framework known as Common Logic —have evolved out of the more practical and applied encounter of FOL with the problem of representing, sharing, and reasoning upon information on the World Wide Web. (shrink)

Knowledge Representation and Reasoning (KR&R) is based on the idea that propositional content can be rigorously represented in formal languages long the province of logic, in such a way that these representations can be productively reasoned over by humans and machines; and that this reasoning can be used to produce knowledge-based systems (KBSs). As such, KR&R is a discipline conventionally regarded to range across parts of artificial intelligence (AI), computer science, and especially logic. This standard view of (...) KR&R’s participating fields is correct — but dangerously incomplete. The view is incomplete because, as we explain herein, sophisticated KR&R must rely heavily upon philosophy. Encapsulated, the reason is actually quite straightforward: Sophisticated KR&R must include the representation of not only simple properties, but also concepts that are routine in the formal sciences (theoretical computer science, mathematics, logic, game theory, etc.), and everyday socio-cognitive concepts like mendacity, deception, betrayal, and evil. Because in KR&R the representation of such concepts must be rigorous in order to enable machine reasoning (e.g., machine-generated and machine-checked proofs that a is lying to b) over them, philosophy, devoted as it is in no small part to supplying analyses of such concepts, is a crucial partner in the overall enterprise. To put the point another way: When the knowledge to be represented is such as to require lengthy formulas in expressive formal languages for that representation, philosophy must be involved in the game. In addition, insofar as the advance of KR&R must allow formalisms and processes for representing and reasoning over visual propositional content, philosophy will be a key contributor into the future. (shrink)

We present a preliminary high-level formal theory, grounded on knowledge representation techniques and foundational ontologies, for the uniform and integrated representation of the different kinds of (quali- tative and quantitative) knowledge involved in the designing process. We discuss the conceptual nature of engineering design by individuating and analyzing the involved notions. These notions are then formally charac- terized by extending the DOLCE foundational ontology. Our ultimate purpose is twofold: (i) to contribute to foundational issues of design; (...) and (ii) to support the development of advanced modelling systems for (qualitative and quantitative) representation of design knowledge. (shrink)

The notion of modularity, introduced by Noam Chomsky and developed with special emphasis on perceptual and linguistic processes by Jerry Fodor in his important book The Modularity of Mind, has provided a significant stimulus to research in cognitive science. This book presents essays in which a diverse group of philosophers, linguists, psycholinguists, and neuroscientists - including both proponents and critics of the modularity hypothesis - address general questions and specific problems related to modularity. Jay L. Garfield is Associate Professor of (...) Philosophy in the School of Communications and Cognitive Science at Hampshire College. (shrink)

© 2017 by the authors. Aristotelian diagrams visualize the logical relations among a finite set of objects. These diagrams originated in philosophy, but recently, they have also been used extensively in artificial intelligence, in order to study various knowledge representation formalisms. In this paper, we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical entities. In particular, we focus on four polyhedral Aristotelian diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron, the tetrakis hexahedron, (...) the tetraicosahedron and the nested tetrahedron. After an in-depth investigation of the geometrical properties and interrelationships of these polyhedral diagrams, we analyze the correlation between logical and geometrical distance in each of these diagrams. The outcome of this analysis is that the Aristotelian rhombic dodecahedron and tetrakis hexahedron exhibit the strongest degree of correlation between logical and geometrical distance; the tetraicosahedron performs worse; and the nested tetrahedron has the lowest degree of correlation. Finally, these results are used to shed new light on the relative strengths and weaknesses of these polyhedral Aristotelian diagrams, by appealing to the congruence principle from cognitive research on diagram design. (shrink)

The focus of this paper will be on the problem of perceptual presence and on a solution to this problem pioneered by Kant [1781; 1783] and refined by Sellars [Sellars, 1978] and Strawson [Strawson, 1971]. The problem of perceptual presence is that of explaining how our perceptual experience of the world gives us a robust sense of the presence of objects in perception over and above those sensory aspects of the object given in perception. Objects possess other properties which are, (...) one might say, phenomenologically present even though they are admittedly sensorily absent. The general form of the solution to this problem that Kant developed seems to me to be a neglected resource in contemporary work on perceptual consciousness. Kant solves the problem of perceptual presence by appealing to that which he called the productive use of the imagination. This faculty of mind supplies schematic representations of the object of perception that explains a phenomenological sense of perceptual presence even of those features that are not, in a sense to be further clarified,. (shrink)