Kurt Friedrich Gödel was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics, building on earlier work by the likes of Richard Dedekind, Georg Cantor and Frege.
Many-valued logic refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values for any proposition. Classical two-valued logic may be extended to n-valued logic for n greater than 2. Those most popular in the literature are three-valued, four-valued, nine-valued, the finite-valued with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic.
Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas:
In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically. Although automated reasoning is considered a sub-field of artificial intelligence, it also has connections with theoretical computer science and philosophy.
Vasant G. Honavar is an Indian born American computer scientist, and artificial intelligence, machine learning, big data, data science, causal inference, knowledge representation, bioinformatics and health informatics researcher and professor.
ACM SIGACT or SIGACT is the Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory, whose purpose is support of research in theoretical computer science. It was founded in 1968 by Patrick C. Fischer.
Keith Leonard Clark is an Emeritus Professor in the Department of Computing at Imperial College London, England.
Moshe Ya'akov Vardi is an Israeli mathematician and computer scientist. He is a Professor of Computer Science at Rice University, United States. He is University Professor, the Karen Ostrum George Professor in Computational Engineering, Distinguished Service Professor, and director of the Ken Kennedy Institute for Information Technology. His interests focus on applications of logic to computer science, including database theory, finite model theory, knowledge in multi-agent systems, computer-aided verification and reasoning, and teaching logic across the curriculum. He is an expert in model checking, constraint satisfaction and database theory, common knowledge (logic), and theoretical computer science.
Ronald Fagin is an American mathematician and computer scientist, and IBM Fellow at the IBM Almaden Research Center. He is known for his work in database theory, finite model theory, and reasoning about knowledge.
Knowledge retrieval seeks to return information in a structured form, consistent with human cognitive processes as opposed to simple lists of data items. It draws on a range of fields including epistemology, cognitive psychology, cognitive neuroscience, logic and inference, machine learning and knowledge discovery, linguistics, and information technology.
Infinity and the Mind: The Science and Philosophy of the Infinite is a popular mathematics book by American mathematician, computer scientist, and science fiction writer Rudy Rucker.
The annual International Web Rule Symposium (RuleML) is an international academic conference on research, applications, languages and standards for rule technologies. Since 2017 it is organised as International Joint Conference on Rules and Reasoning (RuleML+RR). It is a conference in the field of rule-based programming and rule-based systems including production rules systems, logic programming rule engines, and business rules engines/business rules management systems; Semantic Web rule languages and rule standards ; rule-based event processing languages (EPLs) and technologies; and research on inference rules, constraint handling rules, transformation rules, decision rules, production rules, and ECA rules. RuleML+RR is the leading conference to build bridges between academia and industry in the field of Web rules and its applications, especially as part of the semantic technology stack. RuleML+RR is commonly listed together with other Artificial Intelligence conferences worldwide.
Henry A. Kautz is a computer scientist, Founding Director of Institute for Data Science and Professor at University of Rochester. He is interested in knowledge representation, artificial intelligence, data science and pervasive computing.
Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how, and savviness often associated with the ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. Humans apply logical intuition in proving mathematical theorems, validating logical arguments, developing algorithms and heuristics, and in related contexts where mathematical challenges are involved. The ability to recognize logical or mathematical truth and identify viable methods may vary from person to person, and may even be a result of knowledge and experience, which are subject to cultivation. The ability may not be realizable in a computer program by means other than genetic programming or evolutionary programming.
In logic, a finite-valued logic is a propositional calculus in which truth values are discrete. Traditionally, in Aristotle's logic, the bivalent logic, also known as binary logic was the norm, as the law of the excluded middle precluded more than two possible values for any proposition. Modern three-valued logic allows for an additional possible truth value.
In logic, an infinite-valued logic is a many-valued logic in which truth values comprise a continuous range. Traditionally, in Aristotle's logic, logic other than bivalent logic was abnormal, as the law of the excluded middle precluded more than two possible values for any proposition. Modern three-valued logic allows for an additional possible truth value and is an example of finite-valued logic in which truth values are discrete, rather than continuous. Infinite-valued logic comprises continuous fuzzy logic, though fuzzy logic in some of its forms can further encompass finite-valued logic. For example, finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification of fuzzy logic.
Pascal Hitzler is a German American computer scientist specializing in Semantic Web and Artificial Intelligence. He is endowed Lloyd T. Smith Creativity in Engineering Chair and Director of the Center for Artificial Intelligence and Data Science at Kansas State University, and the founding Editor-in-Chief of the Semantic Web journal and the IOS Press book series Studies on the Semantic Web.
Michael Genesereth is an American logician and computer scientist, who is most known for his work on computational logic and applications of that work in enterprise management, computational law, and general game playing. Genesereth is professor in the Computer Science Department at Stanford University and a professor by courtesy in the Stanford Law School. His 1987 textbook on Logical Foundations of Artificial Intelligence remains one of the key references on Symbolic artificial intelligence. He is the author of the influential Game Description Language (GDL) and Knowledge Interchange Format (KIF), the latter of which led to the ISO Common Logic standard.
