This book introduces the properties of conservative extensions of First Order Logic (FOL) to new Intensional First Order Logic (IFOL). This extension allows for intensional semantics to be used for concepts, thus affording new and more intelligent IT systems. Insofar as it is conservative, it preserves software applications and constitutes a fundamental advance relative to the current RDB databases, Big Data with NewSQL, Constraint databases, P2P systems, and Semantic Web applications. Moreover, the many-valued version of IFOL can support the AI applications based on many-valued logics.

There is a growing interest in programming languages and systems based on nonclassical logics such as temporal logics, interval logics, modal and intuitionistic logics. In fact, a whole new programming paradigm called 'intensional programming' has been created, with applications in a wide range of areas, including parallel programming, dataflow computation, temporal reasoning, scientific computation, real-time programming, temporal and multidimensional databases, spreadsheets, attribute grammars, and Internet programming. This volume presents ongoing research as well as future directions of this new and fascinating area of research.

Although the two volumes of Logic, Language, and Meaning can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions.

This book provides a systematic study of three foundational issues in the semantics of natural language that have been relatively neglected in the past few decades. focuses on the formal characterization of intensions, the nature of an adequate type system for natural language semantics, and the formal power of the semantic representation language proposes a theory that offers a promising framework for developing a computational semantic system sufficiently expressive to capture the properties of natural language meaning while remaining computationally tractable written by two leading researchers and of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language

The essays in this book deal with a number of problems in the analysis of intensional language - more especially with the analysis of the personal modalities in natural language. Together they cover a representative spectrum of the problems of contemporary ,interest in this area, in a way that should make them of interest to linguists, logicians and philosophers concerned with natural language. The contributors are mostly more linguists than logicians or philosophers but some are more logicians or philosophers than linguists. As far as possible, we have tried to conduct the discussion in terms that will enable students from any of these fields to come to grips with the central issues. This volume will provide, I think, material for a very stimulating course. I have used it as the basis for a course at the introductory level in the philosophy of language. The essays in the book led us back to look at the classic texts and a good deal of the intervening literature crept in of its own accord. Out of that experience grew the introduction that follows. In contrast with the rest of the book, the introduction is frankly pedagogical. I hope and believe that many who would otherwise find the papers themselves hard to digest will ~e helped on their way by that summary.

Extensional Constructs in Intensional Type Theory presents a novel approach to the treatment of equality in Martin-Loef type theory (a basis for important work in mechanised mathematics and program verification). Martin Hofmann attempts to reconcile the two different ways that type theories deal with identity types. The book will be of interest particularly to researchers with mainly theoretical interests and implementors of type theory based proof assistants, and also fourth year undergraduates who will find it useful as part of an advanced course on type theory.

North-Holland Mathematics Studies, 19: Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics focuses on an approach to the problem of providing a precise account of natural language syntax and semantics, including the set-theoretic semantical methods, Boolean models, and two-sorted type theory. The book first offers information on intensional logic and alternative formulations of intensional logic. Topics include two-sorted type theory, normal forms, extensions and intensional logic, modal T-logic, persistence in intensional logic, generalized completeness of intensional logic, and natural language and intensional logic. The text then examines higher-order modal logic and algebraic semantics. Discussions focus on Cohen's independence results, topological models of MLp, modal independence results, Boolean models of MLp, relative strength of intensional logic and MLp, propositional operators, modal predicate logic, and propositions in MLp. The monograph is a valuable reference for mathematicians and researchers interested in intensional and higher-order modal logic.