The Logic of Information

Philosophy of Information, 2008

Natural Language Engineering, 1997

Logic and Information is an accessible introduction to situation theory and an insightful extension to Barwise and Perry's (1983) original work. It aims to develop the mathematics required for a science of information. So, this is indeed mostly a mathematical logic text, but an interdisciplinary one. There are topics that appeal to philosophers, linguists, computer scientists and cognitive scientists. The clear and illustrative style of the book makes it understandable both to students and more advanced researchers taking new interdisciplinary directions. Devlin states that the basic ideas of situation theory have not changed much since the first hardback edition of the book in 1991. (This paperback edition is the same as the original except for correction of typos.) However, he suggests various additional reading paths for those who want to pursue the recent mathematical developments in the field. Chapter 1 starts with an examination of how one can go about understanding information in the '' Age of Information ''. Devlin emphasizes an empirical approach, developing the mathematical devices when needed as opposed to adopting a form of logic top-down for the same purpose. A historical and critical account of classical logic, based on truth, is given from this point of view. Classical first-order predicate logic is foreseen as a constrained version of the logic of information to be developed. Two important concepts of the theory are introduced : Infons, discrete items of information ; and situations, some limited portion of the whole world linked with constraints. Analogies with other branches of mathematics and science are made liberally throughout the book. An account of cognition in terms of information is given in chapter 2, where the basic ontology of the theory is introduced. This chapter forms, if you like, a requirements specification of the theory being designed. The basic capability of agents to individuate (or discriminate) objects in their environment leads to the definition of a unit of information (an infon) as a tuple that shows whether a number of objects do or do not stand as arguments to a relation. An item of information can be true of a situation, hence is said to be supported by it. Individuation of a situation does not require its exact description to be known, however. Various theory-internal abstractions are underlined in this chapter. Taking representationconstraint pairs related with information as equivalence classes that denote an infon is one such point. Models (in this case set-theoretic) are not to be confused with the real world. More complex concepts of the theory are introduced in chapter 3. One such concept is the introduction of types as a way of detecting higher-order uniformities across situations and other objects of the theory. Related with this are parameters to denote arbitrary objects of a given type, and anchors to assign values to parameters. Examples of parameters in natural language are given in the form of pronouns or proper names. With the introduction of typeabstraction, a situation supporting a set of infons is shown to be a proposition : a claim about the world that a certain object is of a certain type. Also introduced is the concept of an oracle : a special situation that concerns a certain object within a set of related parametric infons. Between accounts of types and oracles, a rather lengthy (and probably redundant) digression is made to question and explain the nature of abstraction and formalism in mathematics.

Journal of the American Society for Information Science and Technology, 2009

Information Science (IS) is commonly said to study collection, classification, storage, retrieval, and use of information. However, there is no consensus on what information is. This article examines some of the formal models of information and informational processes, namely, Situation Theory and Shannon's Information Theory, in terms of their suitability for providing a useful framework for studying information in IS. It is argued that formal models of information are concerned with mainly ontological aspects of information, whereas IS, because of its evaluative role with respect to semantic content, needs an epistemological conception of information. It is argued from this perspective that concepts of epistemological/aesthetic/ethical information are plausible, and that information science needs to rise to the challenge of studying many different conceptions of information embedded in different contexts. This goal requires exploration of a wide variety of tools from philosophy and logic.

tripleC: Communication, Capitalism & Critique. Open Access Journal for a Global Sustainable Information Society, 2009

One of the multiple meanings of the word ‘information’ is given implicitly in the postulates and conditions of information-theoretic logic (I-T-L). The tradition of looking at logical phenomena from an informational stance goes back as far as the XIX century. Logicians such as Boole, De Morgan, Jevons, and Venn already suggested that deducing is a sort of unpacking the information already contained in given premises. In the XX century this tradition is recovered by Carnap and Bar Hillel, Cohen and Nagel, and more recently by Corcoran. John Corcoran has articulated a specific information-theoretic viewpoint of logic with its own particular characteristics. I intend to explain the basic ideas of I-T-L by motivating their philosophical underpinnings. One desideratum is to complement and to shed light on some of the philosophical shortcomings of the nowadays paradigmatic model-theoretic concept of logical consequence. Another is to provide a brief sample of questions to be newly address...

Synthese, 2010

In “General Information in Relevant Logic” (Synthese 167, 2009), the semantics for relevant logic is interpreted in terms of objective information. Objective information is potential data that is available in an environment. This paper explores the notion of objective information further. The concept of availability in an environment is developed and used as a foundation for the semantics, in particular, as a basis for the understanding of the information that is expressed by relevant implication. It is also used to understand the nature of misinformation. A form of relevant logic—called “LOI” for “logic of objective information”—is presented and the relationship between the justification of its proof theory and the semantics is discussed. This relationship is rather reciprocal. Intuitive features of the logic are used to interpret and justify aspects of the model theory and intuitive aspects of the model theory are used to interpret and justify features of the logic. Information conditions are presented for the connectives and the way that they fit into the theory of information is discussed.

Logic and Logical Philosophy, 2013

To better understand what information is and to explain information-related issues has become an essential philosophical task. General concepts from science, ethics and sociology are insufficient. As noted by Floridi, a new philosophy, a Philosophy of Information (PI), is needed. In the 80's, Wu Kun proposed a "The Basic Theory of the Philosophy of Information", which became available in English only in 2010. Wu and Joseph Brenner then found that the latter's non-standard "Logic in Reality" provided critical logical support for Wu's theory. In Part I of our paper, we outline the two basic theories as a metaphilosophy and metalogic for information. We offer our two theories as a further contribution to an informational paradigm. In Part II [WuB14], we develop the relation between information and social value as a basis for the ethical development of the emerging Information Society.

In memory of Alfred Tarski 1901-1983 and Alonzo Church 1903-1995 on the 40th anniversary of their classic works: Logic, Semantics, Metamathematics and Introduction to Mathematical Logic. Information-theoretic approaches [114] to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity.

In this paper I look at Fred Dretske’s account of information and knowledge as developed in Knowledge and The Flow of Information. In particular, I translate Dretske’s probabilistic definition of information to a modal logical framework and subsequently use this to explicate the conception of information and its flow which is central to his account, including the notions of channel conditions and relevant alternatives. Some key products of this task are an analysis of the issue of information closure and an investigation into some of the logical properties of Dretske’s account of information flow.

2005

We discuss how issues of information and computation interact with logic today, and what might be a natural extended agenda of investigation. In particular, the discussion ranges from local dynamics of communication ('update logics') via belief revision systems to the logic of long-term processes over time.