A General Algebraic Semantics for Sentential Logics PDF Download
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Author: Josep Maria Font
Publisher: Cambridge University Press
ISBN: 1316739295
Category : Mathematics
Languages : en
Pages : 160
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Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the seventh publication in the Lecture Notes in Logic series, Font and Jansana develop a very general approach to the algebraization of sentential logics and present its results on a number of particular logics. The authors compare their approach, which uses abstract logics, to the classical approach based on logical matrices and the equational consequence developed by Blok, Czelakowski, Pigozzi and others. This monograph presents a systematized account of some of the work on the algebraic study of sentential logics carried out by the logic group in Barcelona in the 1970s.
Author: Josep Maria Font
Publisher: Cambridge University Press
ISBN: 1316739295
Category : Mathematics
Languages : en
Pages : 160
Get Book Here
Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the seventh publication in the Lecture Notes in Logic series, Font and Jansana develop a very general approach to the algebraization of sentential logics and present its results on a number of particular logics. The authors compare their approach, which uses abstract logics, to the classical approach based on logical matrices and the equational consequence developed by Blok, Czelakowski, Pigozzi and others. This monograph presents a systematized account of some of the work on the algebraic study of sentential logics carried out by the logic group in Barcelona in the 1970s.
Author: Ernest G. Manes
Publisher: Springer Science & Business Media
ISBN: 1461249627
Category : Computers
Languages : en
Pages : 358
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Book Description
In the 1930s, mathematical logicians studied the notion of "effective comput ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.
Author: Irène Guessarian
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 182
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Book Description
Author: Joseph Goguen
Publisher: MIT Press
ISBN: 9780262071727
Category : Computers
Languages : en
Pages : 248
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Book Description
Algebraic Semantics of Imperative Programs presents a self-contained and novel executable introduction to formal reasoning about imperative programs. The authors' primary goal is to improve programming ability by improving intuition about what programs mean and how they run. The semantics of imperative programs is specified in a formal, implemented notation, the language OBJ; this makes the semantics highly rigorous yet simple, and provides support for the mechanical verification of program properties. OBJ was designed for algebraic semantics; its declarations introduce symbols for sorts and functions, its statements are equations, and its computations are equational proofs. Thus, an OBJ program is an equational theory, and every OBJ computation proves some theorem about such a theory. This means that an OBJ program used for defining the semantics of a program already has a precise mathematical meaning. Moreover, standard techniques for mechanizing equational reasoning can be used for verifying axioms that describe the effect of imperative programs on abstract machines. These axioms can then be used in mechanical proofs of properties of programs. Intended for advanced undergraduates or beginning graduate students, Algebraic Semantics of Imperative Programs contains many examples and exercises in program verification, all of which can be done in OBJ.
Author: M. Nivat
Publisher: CUP Archive
ISBN: 9780521267939
Category : Computers
Languages : en
Pages : 664
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Book Description
This book, which contains contributions from leading researchers in France, USA and Great Britain, gives detailed accounts of a variety of methods for describing the semantics of programming languages, i.e. for attaching to programs mathematical objects that encompass their meaning. Consideration is given to both denotational semantics, where the meaning of a program is regarded as a function from inputs to outputs, and operational semantics, where the meaning includes the sequence of states or terms generated internally during the computation. The major problems considered include equivalence relations between operational and denotational semantics, rules for obtaining optimal computations (especially for nondeterministic programs), equivalence of programs, meaning-preserving transformations of programs and program proving by assertions. Such problems are discussed for a variety of programming languages and formalisms, and a wealth of mathematical tools is described.
Author: Josep Maria Font
Publisher: Cambridge University Press
ISBN: 1107167973
Category : Mathematics
Languages : en
Pages : 159
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Book Description
An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group.
Author: Hartmut Ehrig
Publisher: Springer Science & Business Media
ISBN: 3642699626
Category : Computers
Languages : en
Pages : 333
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Book Description
The aim of this book is to present fundamentals of algebraic specifications with respect to the following three aspects: fundamentals in the sense of a carefully motivated introduction to algebraic specifications, which is easy to understand for computer scientists and mathematicians; fundamentals in the sense of mathematical theories which are the basis for precise definitions, constructions, results, and correctness proofs; and fundamentals in the sense of concepts, which are introduced on a conceptual level and formalized in mathematical terms. The book is equally suitableas a text book for graduate courses and as a reference for researchers and system developers.
Author: Godehard Link
Publisher: Stanford Univ Center for the Study
ISBN: 9781575860909
Category : Language Arts & Disciplines
Languages : en
Pages : 432
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Book Description
An analysis of the structural properties of collections or pluralities, homogeneous objects like water, and the semantics and philosophy of events.
Author: Jair Minoro Abe
Publisher: Springer
ISBN: 3319179128
Category : Technology & Engineering
Languages : en
Pages : 195
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Book Description
This book is written as an introduction to annotated logics. It provides logical foundations for annotated logics, discusses some interesting applications of these logics and also includes the authors' contributions to annotated logics. The central idea of the book is to show how annotated logic can be applied as a tool to solve problems of technology and of applied science. The book will be of interest to pure and applied logicians, philosophers and computer scientists as a monograph on a kind of paraconsistent logic. But, the layman will also take profit from its reading.
Author: R.L. Epstein
Publisher: Springer Science & Business Media
ISBN: 9400905254
Category : Philosophy
Languages : en
Pages : 403
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Book Description
This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.
