Formal systemA formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
LogicLogic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language.
Modal logicModal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula can be used to represent the statement that is known. In deontic modal logic, that same formula can represent that is a moral obligation. Modal logic considers the inferences that modal statements give rise to.
Philosophy of logicPhilosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines.
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.
SleepSleep is a state of reduced mental and physical activity in which consciousness is altered and sensory activity is inhibited to a certain extent. During sleep, there is a decrease in muscle activity, and interactions with the surrounding environment. While sleep differs from wakefulness in terms of the ability to react to stimuli, it still involves active brain patterns, making it more reactive than a coma or disorders of consciousness. Sleep occurs in repeating periods, during which the body alternates between two distinct modes: REM and non-REM sleep.
Sleep deprivationSleep deprivation, also known as sleep insufficiency or sleeplessness, is the condition of not having adequate duration and/or quality of sleep to support decent alertness, performance, and health. It can be either chronic or acute and may vary widely in severity. Acute sleep deprivation is when an individual sleeps less than usual or does not sleep at all for a short period of time – normally lasting one to two days but tends to follow the sleepless pattern for longer with no outside factors in play.
Sleep medicineSleep medicine is a medical specialty or subspecialty devoted to the diagnosis and therapy of sleep disturbances and disorders. From the middle of the 20th century, research has provided increasing knowledge of, and answered many questions about, sleep–wake functioning. The rapidly evolving field has become a recognized medical subspecialty in some countries. Dental sleep medicine also qualifies for board certification in some countries. Properly organized, minimum 12-month, postgraduate training programs are still being defined in the United States.
Sleep studyA sleep study is a test that records the activity of the body during sleep. There are five main types of sleep studies that use different methods to test for different sleep characteristics and disorders. These include simple sleep studies, polysomnography, multiple sleep latency tests (MSLTs), maintenance of wakefulness tests (MWTs), and home sleep tests (HSTs). In medicine, sleep studies have been useful in identifying and ruling out various sleep disorders.
Polyphasic sleepPolyphasic sleep is the practice of sleeping during multiple periods over the course of 24 hours, in contrast to monophasic sleep, which is one period of sleep within 24 hours. Biphasic (or diphasic, bifurcated, or bimodal) sleep refers to two periods, while polyphasic usually means more than two. Segmented sleep and divided sleep may refer to polyphasic or biphasic sleep, but may also refer to interrupted sleep, where the sleep has one or several shorter periods of wakefulness, as was the norm for night sleep in pre-industrial societies.
Neuroscience of sleepThe neuroscience of sleep is the study of the neuroscientific and physiological basis of the nature of sleep and its functions. Traditionally, sleep has been studied as part of psychology and medicine. The study of sleep from a neuroscience perspective grew to prominence with advances in technology and the proliferation of neuroscience research from the second half of the twentieth century. The importance of sleep is demonstrated by the fact that organisms daily spend hours of their time in sleep, and that sleep deprivation can have disastrous effects ultimately leading to death in animals.
