Mathematics : Logic

An insightful overview of how syntactic theory was influenced by developments in the formal sciences during the twentieth century. Discusses their implications for the work of linguists at that time, outlines their consequences for current syntactic theory, and provides a groundbreaking reassessment of Chomsky's early work in Generative Grammar. more...

Price: $80.00

Surveys, tutorials, and selected research papers on recent advances in logic. more...

Price: $60.00

Covers the first fifty years of the development of mathematical logic in the 20th century. This title focuses on the achievements of the great names of the period; Russell, Post, Godel, Tarski, Church, and the like. It is suitable for senior undergraduates, graduate students and researchers in the history of logic and various other disciplines. more...

Price: $260.00

Blackline master math activity book jam packed with adventures of monsters, mad types and misfits in a mad and magical mathematical land. Will provide a high level of interest for students as they work through the problems in this book. The problem solving activities will prove thoroughly stimulating to the children in your class. more...

Price: $7.95

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called “left non-monotonicity”, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called “right non-monotonicity”, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in poin more...

Price: $225.00