Automated theorem proving is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science.
Information retrieval (IR) in computing and information science is the process of obtaining information system resources that are relevant to an information need from a collection of those resources. Searches can be based on full-text or other content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for the metadata that describes data, and for databases of texts, images or sounds.
In computer science, formal methods are mathematically rigorous techniques for the specification, development, analysis, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.
The QED manifesto was a proposal for a computer-based database of all mathematical knowledge, strictly formalized and with all proofs having been checked automatically.
Tacit knowledge or implicit knowledge—as opposed to formalized, codified or explicit knowledge—is knowledge that is difficult to express or extract; therefore it is more difficult to transfer to others by means of writing it down or verbalizing it. This can include motor skills, personal wisdom, experience, insight, and intuition.
Software development is the process used to conceive, specify, design, program, document, test, and bug fix in order to create and maintain applications, frameworks, or other software components. Software development involves writing and maintaining the source code, but in a broader sense, it includes all processes from the conception of the desired software through the final manifestation, typically in a planned and structured process often overlapping with software engineering. Software development also includes research, new development, prototyping, modification, reuse, re-engineering, maintenance, or any other activities that result in software products.
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.
In artificial intelligence, symbolic artificial intelligence is the term for the collection of all methods in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, logic and search. Symbolic AI used tools such as logic programming, production rules, semantic nets and frames, and it developed applications such as knowledge-based systems, symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to seminal ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and reasoning systems.
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer.
Computer-aided production engineering (CAPE) is a relatively new and significant branch of engineering. Global manufacturing has changed the environment in which goods are produced. Meanwhile, the rapid development of electronics and communication technologies has required design and manufacturing to keep pace.
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.
Andrzej Wojciech Trybulec was a Polish mathematician and computer scientist noted for work on the Mizar system.
The following outline is provided as an overview of and topical guide to thought (thinking):
The mutilated chessboard problem is a tiling puzzle posed by Max Black in 1946 that asks:
Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares?
Logic Theorist is a computer program written in 1956 by Allen Newell, Herbert A. Simon, and Cliff Shaw. It was the first program deliberately engineered to perform automated reasoning, and has been described as "the first artificial intelligence program". Logic Theorist proved 38 of the first 52 theorems in chapter two of Whitehead and Russell's Principia Mathematica, and found new and shorter proofs for some of them.
Michael Kohlhase is a German computer scientist and professor at University of Erlangen–Nuremberg, where he is head of the KWARC research group.
There is a large body of knowledge that designers call upon and use during the design process to match the ever-increasing complexity of design problems. Design knowledge can be classified into two categories: product knowledge and design process knowledge.
Business process management (BPM) is the discipline in which people use various methods to discover, model, analyze, measure, improve, optimize, and automate business processes. Any combination of methods used to manage a company's business processes is BPM. Processes can be structured and repeatable or unstructured and variable. Though not required, enabling technologies are often used with BPM.
The progression of both the nature of mathematics and individual mathematical problems into the future is a widely debated topic - many past predictions about modern mathematics have been misplaced or completely false, so there is reason to believe that many predictions today will follow a similar path. However, the subject still carries an important weight and has been written about by many notable mathematicians. Typically, they are motivated by a desire to set a research agenda to direct efforts to specific problems, or a wish to clarify, update and extrapolate the way that subdisciplines relate to the general discipline of mathematics and its possibilities. Examples of agendas pushing for progress in specific areas in the future, historical and recent, include Felix Klein's Erlangen program, Hilbert's problems, Langlands program, and the Millennium Prize Problems. In the Mathematics Subject Classification section 01Axx History of mathematics and mathematicians, subsection 01A67 is titled Future prospectives.
Security information and event management (SIEM) is a field within the field of computer security, where software products and services combine security information management (SIM) and security event management (SEM). They provide real-time analysis of security alerts generated by applications and network hardware. Vendors sell SIEM as software, as appliances, or as managed services; these products are also used to log security data and generate reports for compliance purposes. The term and the initialism SIEM was coined by Mark Nicolett and Amrit Williams of Gartner in 2005.
