Ebook: Beyond Two: Theory and Applications of Multiple-Valued Logic

This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

---

This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

---

This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.
Content:
Front Matter....Pages I-X
Front Matter....Pages 1-1
Algebras for Hazard Detection....Pages 3-24
An Abstract Algebraic Logic View of Some Mutiple-valued Logics....Pages 25-57
Representation Theorems and the Semantics of Non-classical Logics, and Applications to Automated Theorem Proving....Pages 59-100
An Algebraic Approach to Entropy and its Generalizations — A Survey....Pages 101-114
Front Matter....Pages 115-115
Classical Gentzen-type Methods in Propositional Many-valued Logics....Pages 117-155
Sequent of Relations Calculi: A Framework for Analytic Deduction in Many-valued Logics....Pages 157-180
Polarity-based Stochastic Local Search Algorithms for Non-clausal Satisfiability....Pages 181-192
Model Checking for Multi-valued Computation Tree Logics....Pages 193-210
Complexity of Many-valued Logics....Pages 211-233
Front Matter....Pages 235-235
Ternary Kleenean Non-additive Measures....Pages 237-250
On the Hierarchy of t-norm Based Residuated Fuzzy Logics....Pages 251-272
A Development of Set Theory in Fuzzy Logic....Pages 273-285
A Fuzzy Generalisation of Information Relations....Pages 287-312
Front Matter....Pages 313-313
Weierstrass Approximation Theorem and ?ukasiewicz Formulas with one Quantified Variable....Pages 315-335
A ?ukasiewicz—style Many-valued Similarity Reasoning. Review....Pages 337-347
Two Values, Three Values, Many Values, No Values....Pages 349-374

---

This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.
Content:
Front Matter....Pages I-X
Front Matter....Pages 1-1
Algebras for Hazard Detection....Pages 3-24
An Abstract Algebraic Logic View of Some Mutiple-valued Logics....Pages 25-57
Representation Theorems and the Semantics of Non-classical Logics, and Applications to Automated Theorem Proving....Pages 59-100
An Algebraic Approach to Entropy and its Generalizations — A Survey....Pages 101-114
Front Matter....Pages 115-115
Classical Gentzen-type Methods in Propositional Many-valued Logics....Pages 117-155
Sequent of Relations Calculi: A Framework for Analytic Deduction in Many-valued Logics....Pages 157-180
Polarity-based Stochastic Local Search Algorithms for Non-clausal Satisfiability....Pages 181-192
Model Checking for Multi-valued Computation Tree Logics....Pages 193-210
Complexity of Many-valued Logics....Pages 211-233
Front Matter....Pages 235-235
Ternary Kleenean Non-additive Measures....Pages 237-250
On the Hierarchy of t-norm Based Residuated Fuzzy Logics....Pages 251-272
A Development of Set Theory in Fuzzy Logic....Pages 273-285
A Fuzzy Generalisation of Information Relations....Pages 287-312
Front Matter....Pages 313-313
Weierstrass Approximation Theorem and ?ukasiewicz Formulas with one Quantified Variable....Pages 315-335
A ?ukasiewicz—style Many-valued Similarity Reasoning. Review....Pages 337-347
Two Values, Three Values, Many Values, No Values....Pages 349-374
....