"Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems..."
Study of logics that do not conform to classical logic, including paraconsistent and relevance logics.
Propositional Logic: Also known as sentential logic or statement logic, this deals with the study of propositions or statements that can either be true or false.
Predicate Logic: Also known as first-order logic or quantificational logic, this extends propositional logic by introducing variables that range over objects in a given domain.
Modal Logic: This includes the study of modalities or modes of truth such as possibility, necessity, contingency and assertion.
Temporal Logic: This includes the study of reasoning about time and events. It deals with temporal operators such as "before", "after", "during", etc.
Deontic Logic: This is the study of obligations, permissions, and prohibitions.
Fuzzy Logic: This is a form of many-valued logic in which truth values are graded rather than binary, allowing for degrees of truth.
Intuitionistic Logic: This is a non-classical logic that rejects the principle of excluded middle, that is, not every proposition must be either true or false.
Paraconsistent Logic: This is a non-classical logic that tolerates contradictions, that is, a set of premises may lead to both a proposition and its negation.
Relevance Logic: This is a non-classical logic that emphasizes the relevance of premises to the conclusion, rather than just their truth value.
Non-monotonic Logic: This is a type of logic where the conclusion can change in the light of new information or premises.
Many-Valued Logic: This is a type of logic where there are more than two truth values possible, such as true, false, and unknown.
Second-order Logic: This extends predicate logic by including quantification over sets, functions, or properties.
Epistemic Logic: This is a type of logic that concerns knowledge and belief, and how they relate to each other.
Game Logic: This is a type of logic that models strategic interactions, where players have incomplete information about the situation.
Infinitary Logic: This extends first-order logic by allowing infinite premises and conclusions.
Autoepistemic Logic: This deals with reasoning about beliefs that can be inferred from a set of beliefs.
Default Logic: This is a non-monotonic logic that involves reasoning with default assumptions or rules.
Relevant Deduction: This is a non-monotonic logic that allows for deduction to be partially based on relevance, rather than just truth values.
Non-associative Logic: This is a type of logic where the basic binary operator is not associative, that is, (a * b) * c is not necessarily equal to a * (b * c).
Quantum Logic: This is a type of logic used in quantum mechanics, which deals with the peculiar features of quantum phenomena such as superposition and entanglement.
Intuitionistic Logic: This is a type of logic that is not based on the principle of excluded middle. It is based on the idea that the truth of a statement can only be established through constructive proof.
Modal Logic: This is a type of logic that is based on the use of modalities, such as possibility, necessity, and impossibility. Modal logic is used to reason about concepts like knowledge, belief, and obligation.
Paraconsistent Logic: This is a type of logic that deals with inconsistent or contradictory information. Paraconsistent logic allows statements that are contradictory to coexist without causing a contradiction.
Relevant Logic: This is a type of logic that is used to reason about relevance. Relevant logic allows for the use of irrelevant information in an argument, but only if it is considered necessary to support the conclusion.
Fuzzy Logic: This is a type of logic that deals with uncertainty and imprecision. Fuzzy logic allows for the use of graded truth values, rather than the binary true/false values used in classical logic.
Many-valued Logic: This is a type of logic that has more than two truth values. Many-valued logic is useful for reasoning about concepts that have more than two mutually exclusive possibilities.
Quantum Logic: This is a type of logic that is used to reason about quantum systems. Quantum logic allows for the use of non-classical probabilities and allows for the existence of true contradictions.
Default Logic: This is a type of logic that is used to reason about default assumptions. Default logic allows for the use of default assumptions, but also allows for exceptions to those assumptions.
Deontic Logic: This is a type of logic that is used to reason about obligation and permission. Deontic logic allows for the use of modalities like "should" and "ought.".
Epistemic Logic: This is a type of logic that is used to reason about knowledge and belief. Epistemic logic allows for the use of modalities like "know" and "believe.".
"...differ in a significant way from standard logical systems such as propositional and predicate logic."
"There are several ways in which this is done, including by way of extensions, deviations, and variations."
"The aim of these departures is to make it possible to construct different models of logical consequence and logical truth."
"Philosophical logic is understood to encompass and focus on non-classical logics..."
"...although the term has other meanings as well."
"In addition, some parts of theoretical computer science can be thought of as using non-classical reasoning..."
"...although this varies according to the subject area."
"...the basic boolean functions (e.g. AND, OR, NOT, etc) in computer science are very much classical in nature..."
"...as is clearly the case given that they can be fully described by classical truth tables."
"...some computerized proof methods may not use classical logic in the reasoning process." Note: The paragraph does not provide sufficient information for the creation of twenty study questions.