Highlights of this volume from the 2004 Annual European Meeting of the Association for Symbolic Logic (ASL) include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect "abstract elementary classes" to issues around p-adic integration.
This is a comprehensive study of the English word 'or', and the logical operators variously proposed to present its meaning. Although there are indisputably disjunctive uses of or in English, it is a mistake to suppose that logical disjunction represents its core meaning. 'Or' is descended from the Anglo-Saxon word meaning second, a form which survives in such expressions as "every other day." Its disjunctive uses arise through metalinguistic applications of an intermediate adverbial meaning which is conjunctive rather than disjunctive (...) in character. These conjunctive uses have puzzled philosophers and logicians, and have been discussed extensively under such headings as "free choice permission." This study examines the textbook myths that have clouded our understanding of how or and other "logical" vocabulary comes to have something approaching its logical meaning in natural languages. It considers the various historical conceptions of disjunction and its place in logic from the Stoics to the present day. (shrink)
This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.
Logic and truth -- Inferences : assessment, recognition, and reconstruction -- Categorical statements and inferences -- Truth-functional statements -- Truth tables and proofs -- Natural deduction -- The logic of quantifiers -- Logic and language -- Applied inductive analysis.
When, if ever, is one justified in accepting the premises of an argument? What is the proper criterion of premise acceptability? Providing a comprehensive theory of premise acceptability, this book answers these questions from an epistemological approach that the author calls "common sense foundationalism". His work will be of interest to specialists in informal logic, critical thinking and argumentation theory as well as to a broader range of philosophers and those teaching rhetoric.
A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional (...) coverage of introductory material such as sets. Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. Reduced mathematical rigour to fit the needs of undergraduate students. (shrink)
Is logic masculine? Is women's lack of interest in the "hard core" philosophical disciplines of formal logic and semantics symptomatic of an inadequacy linked to sex? Is the failure of women to excel in pure mathematics and mathematical science a function of their inability to think rationally? Andrea Nye undermines the assumptions that inform these questions, assumptions such as: logic is unitary, logic is independenet of concrete human relations, and logic transcends historical circumstances as well as gender. In a series (...) of studies of the logics of historical figures--Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege--she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, or scientists. (shrink)
Medieval Modal Logic & Science uses modal reasoning in a new way to fortify the relationships between science, ethics, and politics. Robert C. Trundle accomplishes this by analyzing the role of modal logic in the work of St. Augustine and St. Thomas Aquinas, then applying these themes to contemporary issues. He incorporates Augustine's ideas involving thought and consciousness, and Aquinas's reasoning to a First Cause. The author also deals with Augustine's ties to Aristotelian modalities of thought regarding science and logic, (...) reassessing the commonly held belief in Augustine's Platonism to not be a mistake as much as a simplistic view of his philosophy. Trundle links contemporary issues in epistemology, morality, theology, and logic, making several useful connections between ancient and medieval studies in modal logic and modern concerns. These applications of modal theory illuminate many puzzles in the works of Heidegger, Wittgenstein, Whitehead, and Kuhn. (shrink)
Logic brings elementary logic out of the academic darkness into the light of day. Paul Tomassi makes logic fully accessible for anyone trying to come to grips with the complexities of this challenging subject. This book is written in a patient and user-friendly way which makes both the nature and value of formal logic crystal clear. This textbook proceeds from a frank, informal introduction to fundamental logical notions to a system of formal logic rooted in the best of our natural (...) deductive reasoning in daily life. The book includes plenty of exercise to put the students' reading to test, summay boxes of key points, a glossary and many illustrations. This book will be useful to any student who needs a patient and comprehensible introduction to what otherwise can be a daunting subject. (shrink)
A-LOGIC is a full-length book (600+ pg). It functions as a system of logic designed to: 1) solve the standard paradoxes and major problems of standard mathematical logic; 2) minimize that logic's anomalies with respect to ordinary language, yet; 3) prove that all theorems in mathematical logic are tautologies. It covers lst order logic the logic of the words "and", "or", "not", "all" and "some". But it also has a non truth functional "if...then" and differs in its definition of validity, (...) its semantics and its theorems. In the book A-logic is contrasted step by step with standard mathematical logic as presented and defended by Quine. All of standard logic's theorems are proven tautologies in A-logic. But some argument-forms called "valid" in standard logic are not valid in A-logic -- notably non-sequiturs like "(P and not-P), therefore Q". In addition A-logic has many tautologies with its non-truthfunctional "if ... then" that standard logic can not derive -- e.g., "Not-(if P&Q then not-P)." A-logic's semantics is based on syntactically defined concepts of logical synonymy and containment of meanings rather than on truth-values and truth-functions. Its "if...then" sentences (called "C-conditionals") are valid if and only if (i) the meaning of the consequent is logically contained in that of the antecedent, and (ii) the antecedent and consequent are jointly consistent. The predicate "valid" holds only of C-conditionals and arguments. No valid C-conditionals are translatable into standard logic though all of them imply tautologies of standard logic. (shrink)
In this book Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals as correctly and completely defining the notion of truth. He offers a comprehensive defense of the semantical theory by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences can be constructed. Yaqub concludes by introducing a logic of truth (...) that further demonstrates the adequacy of this theory. (shrink)
This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity of Russell's (...) philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism. (shrink)
However, if we take a more generous view about possibility, then more alternatives present themselves. The best of these may be something that we formerly took to be impossible, and which is better than the best of the earlier possibilities.
In this book, Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals (such as "The sentence 'Johannes loved Clara' is true if and only if Johannes loved Clara") as correctly and completely defining the notion of truth. The semantical theory, which is called the revision theory, that emerges from this conception paints a metaphysical picture of truth (...) as a property whose applicability is given by a revision process rather than by a fixed extension. The main advantage of this revision process is its ability to explain why truth seems in many cases almost redundant, in others substantial, and yet in others paradoxical (as in the famous Liar). Yaub offers a comprehensive defense of the revision theory of truth by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences (Liar and company) can be constructed. Yaqub concludes by introducing a logic of truth that further demonstrates the adequacy of the revision theory. (shrink)
The International workshop 'Frontiers of Combining Systems' is the only forum that is exclusively devoted to research efforts in this interdisciplinary area. This volume contains selected, edited papers from the second installment of the workshop. The contributions range from theorem proving, rewriting and logic to systems and constraints. While there is a clear emphasis on automated tools and logics, the contributions to this volume show that there exists a rapidly expanding body of solutions of particular instances of the combination problem, (...) and at the same time, that the issue of developing general frameworks for intergrating formalisms and systems is taking on an increasingly important position on the international research agenda. The idea of combining formal systems and algorithms has been attracting interest in areas as diverse as constraint logic programming, automated deduction, verification, information retrieval, computational linguistics, artificial intelligence, and logic. As any interesting real world system is a complex composite entity, decomposing its descriptive requirements (for design, verification, or maintenance purposes) into simpler, more restricted tasks is appealing as it is often the only plausible way of tackling complex modelling problems. A core body of notions, questions and results is beginning to emerge in the area, and we are beginning to understand the computational and logical impact of combining methods and algorithms. (shrink)
Logic With Trees is a new and original introduction to modern formal logic. It contains discussions on philosophical issues such as truth, conditionals and modal logic, presenting the formal material with clarity, and preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and exercises guide beginners through the book, with answers to selected exercises enabling readers to check their progress. Logic With Trees equips students with: a complete and clear account of the truth-tree system for first order logic; (...) the importance of logic and its relevance to many different disciplines; the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic; the ability to contest claims that "ordinary" reasoning is well represented by formal first order logic. (shrink)
Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems.The logical systems presented are:- Propositional calculus (including binary decision diagrams);- Predicate calculus;- Resolution;- Hoare logic;- Z;- (...) Temporal logic.Answers to exercises (for instructors only) as well as Prolog source code for algorithms may be found via the Springer London web site: http://www.springer.com/978-1-85233-319-5 Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He is the author of numerous textbooks on concurrency, programming languages and logic, and has developed software tools for teaching concurrency. In 2004, Ben-Ari received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education. (shrink)
Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw (...) upon the concepts and principles presented in the first section. Numerous exercises and an introduction to the theory of real numbers are also presented. Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject. (shrink)
A demanding introduction to logic and critical thinking, this book offers more traditional means of teaching the art of reasoning at a time when the field has become almost mathematical. Francis Dauer has rethought the framework for teaching reasoning in general and formal logic in particular, the desired epistemological context, and the role of the fallacies. The result is a coherent and very readable work, informed by Dauer's extensive experience teaching and writing on the subject.
The purpose of this book is to develop a framework for analyzing strategic rationality, a notion central to contemporary game theory, which is the formal study of the interaction of rational agents, and which has proved extremely fruitful in economics, political theory, and business management. The author argues that a logical paradox (known since antiquity as "the Liar paradox") lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to (...) establish some kind of reputation. Building on the work of Parsons, Burge, Gaifman, and Barwise and Etchemendy, Robert Koons constructs a context-sensitive solution to the whole family of Liar-like paradoxes, including, for the first time, a detailed account of how the interpretation of paradoxial statements is fixed by context. This analysis provides a new understanding of how the rational agent model can account for the emergence of rules, practices, and institutions. (shrink)
Lewis, D. Semantic analyses for dyadic deontic logic.--Salomaa, A. Some remarks concerning many-valued propositional logics.--Chellas, B. F. Conditional obligation.--Jeffrey, R.C. Remarks on interpersonal utility theory.--Hintikka, J. On the proper treatment of quantifiers in Montague semantics.--Mayoh, B.H. Extracting information from logical proofs.--Åqvist, L. A new approach to the logical theory of actions and causality.--Pörn, I. Some basic concepts of action.--Bouvère, K. de. Some remarks concerning logical and ontological theories.--Hacking, I. Combined evidence.--Äberg, C. Solution to a problem raised by Stig Kanger and (...) a set theoretical statement equivalent to the axiom of choice.--Lindström, P. On characterizing elementary logic.--Scott, D. Rules and derived rules.--Hansson, B. A program for pragmatics.--Hermerén, G. Models.--Fenstad, J.E. Remarks on logic and probability.--Stenlund, S. Analytic and synthetic arithmetical statements. (shrink)
Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka’s independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic (...) semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic. (shrink)
In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic (...) and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists. (shrink)
Introduction: Major terms, their classification, and their relation to the book's objective -- The problem of analogous forms -- Natural logic, categories, and the individual -- Shift to individual categories, dynamics, and a psychological look at identity form versus function -- What is the difference between the logic governing a figure of speech and the logic that is immature or unconscious? -- What are the role and function of the self vis-à-vis consciousness? -- Development in the logic from immature to (...) mature modes -- Pathological and defensive logical forms -- The "I," identity, and the part-whole resolutions -- The "I," entropy, and the trope. (shrink)
The classic results obtained by Gödel, Tarski, Kleene, and Church in the early thirties are the finest flowers of symbolic logic. They are of fundamental importance to those investigations of the foundations of mathematics via the concept of a formal system that were inaugurated by Frege, and of obvious significance to the mathematical disciplines, such as computability theory, that developed from them. Derived from courses taught by the author over several years, this new exposition presents all of the results with (...) their original proofs and central concepts in a manner that is unified by a systematic grounding of the notion of effectiveness in the semantics of the existential quantifier. Logicians and non-mathematicians, repelled by detail which is not obviously relevant in the standard textbooks, will be able to reach the heart of the matter with a minimum of fuss. (shrink)