John Etchemendy

Tarski on truth and logical consequence

Tarskis writings on the concepts of truth and logical consequence rank among the most influential works in both logic and philosophy of the twentieth century. Because of this, it would be impossible to give a careful and accurate account of how far that influence reaches and of the complex route by which it spread. In logic, Tarskis methods of defining satisfaction and truth, as well as his work pioneering general model-theoretic techniques, have been entirely absorbed into the way the subject is presently done; they have become part of the fabric of contemporary logic, material presented in the initial pages of every modern textbook on the subject. In philosophy, the influence has been equally pervasive, extending not only to work in semantics and the philosophies of logic and language, but to less obviously allied areas such as epistemology and the philosophy of science as well. Rather than try to chart the wide-ranging influence of these writings or catalog the important research they have inspired, I will concentrate on various confusions and misunderstandings that continue to surround this work. For in spite of the extensive attention the work has received in the past fifty years, especially in the philosophical literature, misunderstandings of both conceptual and historical sorts are still remarkably widespread. Indeed in the philosophical community, recent reactions to Tarskis work on truth range from Karl Poppers “intense joy and relief” at Tarskis “legitimation” of the notion [1974, p. 399], to Hilary Putnams assessment that “as a philosophical account of truth, Tarskis theory fails as badly as it is possible for an account to fail” [1985, p. 64]. Opinions have not exactly converged.

Openproof - A Flexible Framework for Heterogeneous Reasoning

In this paper we describe the Openproof heterogeneous reasoning framework. The Openproof framework provides support for the implementation of heterogeneous reasoning environments, i.e., environments for writing arguments or proofs involving a number of different kinds of representation. The resulting environments are in a similar spirit to our Hyperproofprogram, though the Openproof framework goes beyond Hyperproofby providing facilities for the inclusion of a variety of representation systems in the same environment. The framework serves as the core of a number of widely used educational programs including Fitch.

A computational architecture for heterogeneous reasoning

In this paper we describe a computational architecture for applications that support heterogeneous reasoning. Heterogeneous reasoning is, in its most general form, reasoning that employs representations drawn from multiple representational forms. Of particular importance, and the principal focus of the architecture, is heterogeneous reasoning which employs one or more forms of graphical representation, perhaps in combination with sentences (of English or another language, whether natural or scientific). Graphical representations include diagrams, pictures, layouts, blueprints, flowcharts, graphs, maps, tables, spreadsheets, animations, video, and 3D models. By ‘an application that supports heterogeneous reasoning’ we mean an application that allows users to construct, record, edit, and replay a process of reasoning using multiple representations so that the structure of the reasoning is maintained and the informational dependencies and justifications of the individual steps of the reasoning can be recorded.

Learning to use the openbox: a framework for the implementation of heterogeneous reasoning

In this tutorial we will present the Openbox, a framework for constructing heterogeneous reasoning systems. Heterogeneous reasoning is reasoning involving multiple representations. A common example is using a map (diagram) together with an address (sentence) to plan a route from one point to another. This kind of reasoning may involve diagrams of multiple types, diagrams and sentences, and/or multiple instances of the same diagram type. Reasoning with sentences, or with a single diagram are special cases of the general heterogeneous setting.

Heterogeneous Reasoning

During the 1990s, we developed the theory of formal heterogeneous deduction: logically valid inference that involves information expressed using multiple different representations. The Hyperproof program was developed as an implementation of that theory, and permitted deductions using sentences of first-order logic and blocks world diagrams.We have since been generalizing both the theory and the implementation to allow applications in a wide variety of domains.

The Concept of Logical Consequence.

Introduction 1. Representational semantics 2. Tarski on logical truth 3. Interpretational semantics 4. Interpreting quantifiers 5. Modality and consequence 6. The reduction principle 7. Substantive generalizations 8. The myth of the logical constant 9. Logic from the metatheory 10. Completeness and soundness Conclusion Notes Bibliography Index.

Representing visual decision making: a computational architecture for heterogeneous reasoning

In this chapter, we describe a computational architecture for applications that support heterogeneous reasoning. Heterogeneous reasoning is, in its most general form, reasoning that employs representations drawn from multiple representational forms. Of particular importance, and the principal focus of this architecture, is heterogeneous reasoning that employs one or more forms of graphical representation, perhaps in combination with sentences (of English or another language, whether natural or scientific). Graphical representations include diagrams, pictures, layouts, blueprints, flowcharts, graphs, maps, tables, spreadsheets, animations, video, and 3D models. By “an application that supports heterogeneous reasoning” we mean an application that allows users to construct, record, edit, and replay a process of reasoning using multiple representations so that the structure of the reasoning is maintained and the informational dependencies and justifications of the individual steps of the reasoning can be recorded. Our architecture is based on the model of natural deduction in formal logic. In this chapter we describe and motivate the modifications to the standard logical model necessary to capture a wide range of heterogeneous reasoning tasks. The resulting generalization forms our computational architecture for heterogeneous reasoning (CAHR).

The Liar--An Essay in Truth and Circularity.

INTRODUCTION: The Liar Sentences, statements, and Propositions The universe of hypersets RUSSELLIAN PROPOSITIONS AND THE LIAR: Modeling Russellian propositions Truth of Russellian propositions Consequences of the Russellian account Sentences and Russellian propositions AUSTINIAN PROPOSITIONS AND THE LIAR: Modeling Austinian propositions Austinian propositions and the world An Austinian semantics Relating the Russellian and Austinian accounts Negation and denial Conclusions Bibliography Index.