'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.
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'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focu...
This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic...
This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due ...
area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management, whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a...
area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logi...
ThisbookdiscusseshowTypeLogicalGrammarcanbemodi?edinsuch awaythatasystematictreatmentofanaphoraphenomenabecomesp- sible without giving up the general architecture of this framework. By Type Logical Grammar, I mean the version of Categorial Grammar that arose out of the work of Lambek, 1958 and Lambek, 1961. There Ca- gorial types are analyzed as formulae of a logical calculus. In particular, the Categorial slashes are interpreted as forms of constructive impli- tion in the sense of Intuitionistic Logic. Such a theory of grammar is per se attractive for a formal linguist who is interested in...
ThisbookdiscusseshowTypeLogicalGrammarcanbemodi?edinsuch awaythatasystematictreatmentofanaphoraphenomenabecomesp- sible without giving up the general ...
The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies.This volume will be of great...
The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach compl...
Abstract In the chapter some preliminary methodological issues are discussed, including the demarcation between logic and linguistics and the shortcomings of empirical base of the theory of syntax. An epistemological approach to language is sketched out and a need for the proper balance between logical aspects of natural language and vernacular usage is claimed crucial for any reliable theory of syntax and - mantics. Learnability and efficiency are presented as the most important c- straints to be imposed upon a logical analysis of language. Keywords Linguistics, Logic, Methodology, Natural...
Abstract In the chapter some preliminary methodological issues are discussed, including the demarcation between logic and linguistics and the shortcom...
A good title should be informative enough to illuminate a potential reader on the content of a book. We hope that the present title gives at least some hints of what this book is about. The notion of natural deduction or modal logic are rather well known, but the notion of hybrid system certainly needs some explanation. In short, this study may be seen as a kind of search for good deductive systems. We think of systems good in practice which may be applied with easenotonlybywelltrainedlogiciansbutalso, forexample, byphilosophers who need handy deductive tools accompanying their analyses. In...
A good title should be informative enough to illuminate a potential reader on the content of a book. We hope that the present title gives at least som...
This book is about proof theory for (the main systems of) modal logic. It is the first book to give a uniform and exhaustive presentation of both types of sequent calculus for modal logic, the purely syntactic sequent calculi as well as the semantic ones.
This book is about proof theory for (the main systems of) modal logic. It is the first book to give a uniform and exhaustive presentation of both t...
Providing a reference for researchers and students, this volume presents the fundamental concepts of dual tableaux, and a wide scope of applications. These include logic methods used in mathematics and philosophy, as well as applied theories of computational logic.
Providing a reference for researchers and students, this volume presents the fundamental concepts of dual tableaux, and a wide scope of applications. ...
Can OUGHT be derived from IS? This book presents an investigation of this time-honored problem by means of alethic-deontic predicate logic. New in this study is the leitmotif of relevance: is-ought inferences indeed exist, but they are all irrelevant in a precise logical sense. New proof techniques establish this result for very broad classes of logics. A profound philosophical analysis of is-ought bridge principles supplements the logical study. The final results imply incisive limitations for the justifiability of ethics as opposed to empirical science.
Can OUGHT be derived from IS? This book presents an investigation of this time-honored problem by means of alethic-deontic predicate logic. New in thi...
