Predicate transformer semanticsPredicate transformer semantics were introduced by Edsger Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs". They define the semantics of an imperative programming paradigm by assigning to each statement in this language a corresponding predicate transformer: a total function between two predicates on the state space of the statement. In this sense, predicate transformer semantics are a kind of denotational semantics.
Adaptive behaviorAdaptive behavior is behavior that enables a person (usually used in the context of children) to cope in their environment with greatest success and least conflict with others. This is a term used in the areas of psychology and special education. Adaptive behavior relates to everyday skills or tasks that the "average" person is able to complete, similar to the term life skills. Nonconstructive or disruptive social or personal behaviors can sometimes be used to achieve a constructive outcome.
Hoare logicHoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician Tony Hoare, and subsequently refined by Hoare and other researchers. The original ideas were seeded by the work of Robert W. Floyd, who had published a similar system for flowcharts. The central feature of Hoare logic is the Hoare triple.
Behavior modificationBehavior modification is an early approach that used respondent and operant conditioning to change behavior. Based on methodological behaviorism, overt behavior was modified with consequences, including positive and negative reinforcement contingencies to increase desirable behavior, or administering positive and negative punishment and/or extinction to reduce problematic behavior. It also used Flooding desensitization to combat phobias.
Positive behavior supportPositive behavior support (PBS) uses tools from applied behaviour analysis and values of normalisation and social role valorisation theory to improve quality of life, usually in schools. PBS uses functional analysis to understand what maintains an individual's challenging behavior and how to support the individual to get these needs met in more appropriate way, instead of using 'challenging behaviours'. People's inappropriate behaviors are difficult to change because they are functional; they serve a purpose for them.
Applied behavior analysisApplied behavior analysis (ABA), also called behavioral engineering, is a psychological intervention that applies empirical approaches based upon the principles of respondent and operant conditioning to change behavior of social significance. It is the applied form of behavior analysis; the other two forms are radical behaviorism (or the philosophy of the science) and the experimental analysis of behavior (or basic experimental laboratory research).
Imperative programmingIn computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program consists of commands for the computer to perform. Imperative programming focuses on describing how a program operates step by step, rather than on high-level descriptions of its expected results.
Procedural programmingProcedural programming is a programming paradigm, derived from imperative programming, based on the concept of the procedure call. Procedures (a type of routine or subroutine) simply contain a series of computational steps to be carried out. Any given procedure might be called at any point during a program's execution, including by other procedures or itself. The first major procedural programming languages appeared circa 1957–1964, including Fortran, ALGOL, COBOL, PL/I and BASIC. Pascal and C were published circa 1970–1972.
Functional programmingIn computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can.
Program analysisIn computer science, program analysis is the process of automatically analyzing the behavior of computer programs regarding a property such as correctness, robustness, safety and liveness. Program analysis focuses on two major areas: program optimization and program correctness. The first focuses on improving the program’s performance while reducing the resource usage while the latter focuses on ensuring that the program does what it is supposed to do.
Declarative programmingIn computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow. Many languages that apply this style attempt to minimize or eliminate side effects by describing what the program must accomplish in terms of the problem domain, rather than describing how to accomplish it as a sequence of the programming language primitives (the how being left up to the language's implementation).
Programming paradigmProgramming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, such as allowing side effects, or whether the sequence of operations is defined by the execution model. Other paradigms are concerned mainly with the way that code is organized, such as grouping a code into units along with the state that is modified by the code.
Purely functional programmingIn computer science, purely functional programming usually designates a programming paradigm—a style of building the structure and elements of computer programs—that treats all computation as the evaluation of mathematical functions. Program state and mutable objects are usually modeled with temporal logic, as explicit variables that represent the program state at each step of a program execution: a variable state is passed as an input parameter of a state-transforming function, which returns the updated state as part of its return value.
Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
First-order logicFirst-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable.
TranslationTranslation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between translating (a written text) and interpreting (oral or signed communication between users of different languages); under this distinction, translation can begin only after the appearance of writing within a language community.
Second-order logicIn logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle).
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.
Correctness (computer science)In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctness, which refers to the input-output behavior of the algorithm (i.e., for each input it produces an output satisfying the specification). Within the latter notion, partial correctness, requiring that if an answer is returned it will be correct, is distinguished from total correctness, which additionally requires that an answer is eventually returned, i.e.
Resolution (logic)In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem. For first-order logic, resolution can be used as the basis for a semi-algorithm for the unsatisfiability problem of first-order logic, providing a more practical method than one following from Gödel's completeness theorem.
