Ivan Chajda Knihy

This volume contains 23 research articles on topics in universal algebra and lattice theory. It continues the series „Contributions to General Algebra“, Volumes 1-13, published from 1979 to 2001. All submitted manuscripts have been refereed by an international board. The papers were presented at the 64th Conferende on General Algebra, May 30 - June 2, 2002, at Palacky University Olomouc, Czech Republic, and at the 65th Conferende on General Algebra, March 21-23, 2003, at Potsdam University, Germany. This book is of interest to research workers in the field of algebra and should also be useful as a reference book for many mathematicians.

This volume contains 36 research articles on topics in universal algebra and lattice theory. It continues the series „Contributions to General Algebra“, Volumes 1-12, published from 1979 to 2000. All submitted manuscripts have been refereed by an international board. The papers were presented at the 60th Conference on General Algebra, June 22-25, 2000, at the University of Technology Dresden, Germany, and at the Summer School '99 on General Algebra and Ordered Sets, August 30 - September 4, 1999, at Velke Karlovice, Czech Republic.

Propositional logics, both classical and non-classical, typically overlook the dimension of time, despite Aristotle's assertion that time significantly influences the truth values of propositions. He illustrated this with the statement "There will be a sea battle tomorrow," which cannot be assigned a truth value today. This limitation led him to conclude that two-valued logic fails to encompass the entirety of human reasoning. As logic evolved, particularly with the advent of computers in the 1940s and the rise of Artificial Intelligence, the ability to evaluate future truth values became crucial for controlling complex systems. This necessity spurred interest in temporal logic, which integrates time as a variable in propositional formulas. Arthur Prior introduced tense logic in the late 1950s, focusing on the interplay between tense and modality. This work includes modal operators alongside traditional truth-functional operators. The aim here is not to fully detail tense logic but to present an algebraic axiomatization of tense logic and its operators. While classical propositional logic was formalized by George Boole using Boolean algebras, subsequent developments have seen intuitionistic logic, many-valued logics, and fuzzy logic formalized through various algebraic structures. This monograph employs algebraic methods to axiomatize tense and modal operators, beginning with quantifiers as developed by P. Halmos and J. D. Rut

Connections between logic and lattices were already mentioned by Garrett Birkhoff in his monograph „Lattice Theory“ published in 1940 and a number of books appeared since then on this topic discussing semilattices and semilattice structures however only marginally. The aim of this monograph is to remedy this situation by concentrating on semilattices and semilattice structures exclusively. The authors also discuss implication logics, but focus on the collection of descriptions and properties of the corresponding algebraic structures. They present many known and new results, in particular on semilattices equipped with supplementary operations such as for example pseudocomplementation or relative pseudocomplementation and their generalizations. This book is of interest for algebraists working on semilattice structures or algebras related to logic as well as for logicians. It is hoped that the book can initiate a further development of the topic and that it can in particular be useful for mathematicians starting to work in semilattice structures.

This volume contains 21 research articles on topics in universal algebra and lattice theory. It continues the series „Contributions to General Algebra“, Volumes 1-10, published from 1979 to 1998. All submitted manuscripts have been refereed by an international board. The papers were presented at the 56th Conference on General Algebra, June 12-14, 1998, at the University of Olomouc, and at the Summer School '98 on Universal Algebra and Ordered Sets, August 31 - September 5, 1998, at Velke Karlovice, Czech Republic.