Method of analytic tableauxIn proof theory, the semantic tableau (tæˈbloʊ,_ˈtæbloʊ; plural: tableaux, also called truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure computed for a logical formula, having at each node a subformula of the original formula to be proved or refuted. Computation constructs this tree and uses it to prove or refute the whole formula. The tableau method can also determine the satisfiability of finite sets of formulas of various logics.
Proof calculusIn mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic. Rules of inference: List of rules that can be employed to prove theorems from axioms and theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics.
Psychology of reasoningThe psychology of reasoning (also known as the cognitive science of reasoning) is the study of how people reason, often broadly defined as the process of drawing conclusions to inform how people solve problems and make decisions. It overlaps with psychology, philosophy, linguistics, cognitive science, artificial intelligence, logic, and probability theory. Psychological experiments on how humans and other animals reason have been carried out for over 100 years. An enduring question is whether or not people have the capacity to be rational.
GoalA goal or objective is an idea of the future or desired result that a person or a group of people envision, plan and commit to achieve. People endeavour to reach goals within a finite time by setting deadlines. A goal is roughly similar to a purpose or aim, the anticipated result which guides reaction, or an end, which is an object, either a physical object or an abstract object, that has intrinsic value. Goal setting Goal-setting theory was formulated based on empirical research and has been called one of the most important theories in organizational psychology.
Lambda calculusLambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing lambda terms and performing reduction operations on them.
Goal settingGoal setting involves the development of an action plan designed in order to motivate and guide a person or group toward a goal. Goals are more deliberate than desires and momentary intentions. Therefore, setting goals means that a person has committed thought, emotion, and behavior towards attaining the goal. In doing so, the goal setter has established a desired future state which differs from their current state thus creating a mismatch which in turn spurs future actions.
Typed lambda calculusA typed lambda calculus is a typed formalism that uses the lambda-symbol () to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered (see kinds below). From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus, but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.
Deep inferenceDeep inference names a general idea in structural proof theory that breaks with the classical sequent calculus by generalising the notion of structure to permit inference to occur in contexts of high structural complexity. The term deep inference is generally reserved for proof calculi where the structural complexity is unbounded; in this article we will use non-shallow inference to refer to calculi that have structural complexity greater than the sequent calculus, but not unboundedly so, although this is not at present established terminology.
Explicit substitutionIn computer science, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution. This is in contrast to the standard lambda calculus where substitutions are performed by beta reductions in an implicit manner which is not expressed within the calculus; the "freshness" conditions in such implicit calculi are a notorious source of errors. The concept has appeared in a large number of published papers in quite different fields, such as in abstract machines, predicate logic, and symbolic computation.
Automated theorem provingAutomated theorem proving (also known as ATP or automated deduction) 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. While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics.
