Harrie De Swart Knihy

This book serves as an introduction to logic, emphasizing its connections with philosophy, mathematics, language, and theoretical computer science. Readers will explore classical logic alongside philosophical variants such as modal, epistemic, deontic, and temporal logic, as well as intuitionistic logic. The initial chapter offers a non-technical overview, while subsequent chapters delve into topics like Propositional Logic, Sets, Predicate Logic, Arithmetic, Gödel’s Incompleteness Theorems, Modal Logic, and the Philosophy of Language. Applications in Prolog, Relational Databases, SQL, and Social Choice Theory, particularly Majority Judgment, are also discussed. Historical developments in logic, including Stoic and Aristotelian traditions, logic in the Middle Ages, and the contributions of Frege, Boole, and De Morgan, are highlighted. The book places significant emphasis on conditionals—material, strict, and relevant implication, entailment, counterfactuals, and conversational implicature—providing ample references for further reading. Each chapter concludes with exercise answers. This recent work (2018) combines rigor, depth, and clarity, making it a valuable resource that transcends a mere introductory text. It invites readers to engage deeply with the diverse themes of logic, blending philosophy and mathematics seamlessly.

This book constitutes the proceedings of the 12 International Conference on Relational and Algebraic Methods in Computer Science, RAMICS 2011, held in Rotterdam, The Netherlands, in May/June 2011. This conference merges the RelMICS (Relational Methods in Computer Science) and AKA (Applications of Kleene Algebra) conferences, which have been a main forum for researchers who use the calculus of relations and similar algebraic formalisms as methodological and conceptual tools. Relational and algebraic methods and software tools turn out to be useful for solving problems in social choice and game theory. For that reason this conference included a special track on Computational Social Choice and Social Software. The 18 papers included were carefully reviewed and selected from 27 submissions. In addition the volume contains 2 invited tutorials and 5 invited talks.

This book constitutes the major results of the EU COST (European Cooperation in the field of Scientific and Technical Research) Action 274: TARSKI - Theory and Applications of Relational Structures as Knowledge Instruments - running from July 2002 to June 2005. The papers are devoted to further understanding of interdisciplinary issues involving relational reasoning by addressing relational structures and the use of relational methods in applicable object domains.

InhaltsverzeichnisInvited Lecture.A Relation-Algebraic Approach to Graph Structure Transformation.Contributed Papers.Emptiness Relations in Property Systems.Pregroups: Models and Grammars.Algebraic Semantics of ER-Models in the Context of the Calculus of Relations. II: Dynamic View.Interpretability of First—Order Dynamic Logic in a Relational Calculus.Relations in GUHA Style Data Mining.Groups in Allegories.Distributed Conceptual Structures.A Computer Algebra Approach to Relational Systems Using Gröbner Bases.Fuzzy Relational Images in Computer Science.A Completeness Theorem for Extended Order Dependencies on Relational Attribute Models in Dedekind Categories.Double Residuated Lattices and Their Applications.Interval Bilattices and Some Other Simple Bilattices.Interactive Systems: From Folklore to Mathematics.Relational Constructions in Goguen Categories.A Subintuitionistic Logic and Some of Its Methods.Implementation of Relational Algebra Using Binary Decision Diagrams.Calculating a Relational Program for Transitive Reductions of Strongly Connected Graphs.Calculating Church-Rosser Proofs in Kleene Algebra.On the Definition and Representation of a Ranking.Tangent Circle Algebras.

InhaltsverzeichnisExtended Abstracts of Invited Lectures. Philosophical Aspects of Computerized Verification of Mathematics. A Science of Reasoning (Extended Abstract). Model Checking: Historical Perspective and Example (Extended Abstract). Comparison of Theorem Provers for Modal Logics — Introduction and Summary. FaCT and DLP. Prover KT4. leanK 2.0. Logics Workbench 1.0. Optimised Functional Translation and Resolution. Benchmark Evaluation of ? KE. Abstracts of the Tutorials. Implementation of Propositional Temporal Logics Using BDDs. Computer Programming as Mathematics in a Programming Language and Proof System CL. Contributed Research Papers. A Tableau Calculus for Multimodal Logics and Some (Un)Decidability Results. Hyper Tableau — The Next Generation. Fibring Semantic Tableaux. A Tableau Calculus for Quantifier-Free Set Theoretic Formulae. A Tableau Method for Interval Temporal Logic with Projection. Bounded Model Search in Linear Temporal Logic and Its Application to Planning. On Proof Complexity of Circumscription. Tableaux for Finite-Valued Logics with Arbitrary Distribution Modalities. Some Remarks on Completeness, Connection Graph Resolution, and Link Deletion. Simplification and Backjumping in Modal Tableau. Free Variable Tableaux for a Logic with Term Declarations. Simplification A General Constraint Propagation Technique for Propositional and Modal Tableaux. A Tableaux Calculus for Ambiguous Quantification. From K