List of topics in logic - AbsoluteAstronomy.com

A

A logical abacus is a mechanical digital computer.Also referred to as a "logical machine", the logical abacus is analogous to the ordinary abacus...

-- Abduction (logic) -- Abductive validation -- Affine logic

Affine logic

Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with weakening....

-- Affirming the antecedent --Affirming the consequent

Affirming the consequent

Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form:#If P, then Q.#Q.#Therefore, P....

-- Antecedent

Antecedent (logic)

An antecedent is the first half of a hypothetical proposition.Examples:* If P, then Q.This is a nonlogical formulation of a hypothetical proposition...

-- Antinomy

Antinomy

Antinomy literally means the mutual incompatibility, real or apparent, of two laws. It is a term used in logic and epistemology....

--
Argument form -- Aristotelian logic -- Axiom

Axiom

In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...

-- Axiomatic system

Axiomatic system

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems...

-- Axiomatization

B

Backward chaining

Backward chaining is an inference method that can be described as working backward from the goal...

-- Barcan formula

Barcan formula

In quantified modal logic, the Barcan formula and the converse Barcan formula syntactically state principles or interchange between quantifiers and modalities; semantically state a relation between domains of possible worlds...

-- Biconditional elimination

Biconditional elimination

Biconditional elimination allows one to infer a conditional from a biconditional: if is true, then one may infer either direction of the biconditional, and ....

-- Biconditional introduction

Biconditional introduction

In mathematical logic, biconditional introduction is the rule of inference that, if B follows from A, and A follows from B, then A if and only if B....

-- Bivalence and related laws -- Boolean algebra (logic) -- Boolean algebra (structure)

C

Categorical logic

Categorical logic is a branch of category theory within mathematics, adjacent to mathematical logic but more notable for its connections to theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor...

-- Clocked logic --Cointerpretability

Cointerpretability

In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the language of T in such a way that S proves every formula whose translation is a theorem of T...

--College logic -- Combinational logic

Combinational logic

In digital circuit theory, combinational logic is a type of digital logic which is implemented by boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the...

-- Combinatory logic

Combinatory logic

Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming...

-- Computability logic

Computability logic

Introduced by Giorgi Japaridze in 2003, computability logic is a research programme and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of truth...

-- Conditional

Conditional

Conditional may refer to:*Causal conditional, if X then Y, where X is a cause of Y*Conditional mood , a verb form in many languages*Conditional probability, the probability of an event A given that another event B has occurred...

-- Conditional proof

Conditional proof

A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent....

-- Conjunction elimination --Conjunction introduction

Conjunction introduction

Conjunction introduction is the inference that, if p is true, and q is true, then the conjunction p and q is true.For example, if it's true that it's raining, and it's true that I'm inside, then it's true that "it's raining and I'm inside"....

-- Conjunctive normal form

Conjunctive normal form

In Boolean logic, a formula is in conjunctive normal form if it is a conjunction of clauses, where a clause is a disjunction of literals.As a normal form, it is useful in automated theorem proving...

-- Consequent

Consequent

A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then".Examples:* If P, then Q.Q is the consequent of this hypothetical proposition....

-- Constructive dilemma

Constructive dilemma

In logic, a constructive dilemma is a formal logical argument that takes the form:Therefore, either Q or S is true.In logical operator notation with three premises P \rightarrow Q R \rightarrow S P \lor R \therefore Q \lor S ....

-- Contradiction

Contradiction

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

-- Contrapositive -- Control logic

Control logic

Control logic is a key part of a software program that controls the operations of the program. The control logic responds to commands from the user, and it also acts on its own to perform automated tasks that have been structured into the program....

-- Converse (logic)

Converse (logic)

In logic, the converse of a categorical or implicational statement is the result of reversing its two parts. For the implication P → Q, the converse is Q → P. For the categorical proposition All S is P, the converse is All P is S. In neither case does the converse necessarily follow from...

-- Converse Barcan formula -- Cotolerance -- Counterfactual conditional

Counterfactual conditional

A counterfactual conditional, subjunctive conditional, or remote conditional, abbreviated , is a conditional statement indicating what would be the case if its antecedent were true...

-- Curry's paradox

Curry's paradox

Curry's paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules...

D

De Morgan's laws -- Deduction theorem

Deduction theorem

In mathematical logic, the deduction theorem is a metatheorem of first-order logic. It is a formalization of the common proof technique in which an implication A → B is proved by assuming A and then proving B from this assumption. The deduction theorem explains why proofs of conditional...

-- Deductive reasoning

Deductive reasoning

Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

-- Degree of truth -- Denying the antecedent

Denying the antecedent

Denying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the form:The name denying the antecedent derives from the premise "not P", which denies the "if" clause of the conditional premise....

-- Deviant logic

Deviant logic

Philosopher Susan Haack uses the term "deviant logic" to describe certain non-classical systems of logic. In these logics,* the set of well-formed formulas generated equals the set of well-formed formulas generated by classical logic....

-- Disjunction elimination

Disjunction elimination

In propositional logic disjunction elimination, or proof by cases, is the inference that, if "A or B" is true, and A entails C, and B entails C, then we may justifiably infer C...

-- Disjunction introduction

Disjunction introduction

Disjunction introduction or Addition is a valid, simple argument form in logic:or in logical operator notation: A \vdash A \or B The argument form has one premise, A, and an unrelated proposition, B...

-- Disjunctive normal form

Disjunctive normal form

In boolean logic, a disjunctive normal form is a standardization of a logical formula which is a disjunction of conjunctive clauses. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if and only if it is a disjunction of one or more...

-- Disjunctive syllogism

Disjunctive syllogism

A disjunctive syllogism, also known as disjunction-elimination and or-elimination , and historically known as modus tollendo ponens,, is a classically valid, simple argument form:where \vdash represents the logical assertion....

-- Double negative

Double negative

A double negative occurs when two forms of negation are used in the same sentence. Multiple negation is the more general term referring to the occurrence of more than one negative in a clause....

-- Double negative elimination

Double negative elimination

In propositional logic, the inference rules double negative elimination allow deriving the double negative equivalent by adding or removing a pair of negation signs...

E

Elimination rule -- End term

End term

The end terms in a categorical syllogism are the major term and the minor term . These two terms appear together in the conclusion and separately with the middle term in the major premise and minor premise, respectively.Example:...

-- Exclusive nor -- Exclusive or -- Existential fallacy

Existential fallacy

The existential fallacy, or existential instantiation, is a logical fallacy in Boolean logic while it is not in Aristotelian logic. In an existential fallacy, we presuppose that a class has members even when we are not explicitly told so; that is, we assume that the class has existential import.An...

-- Existential quantification

Existential quantification

In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ , which is called the existential quantifier...

F

Fallacy of distribution

A fallacy of distribution is a logical fallacy occurring when an argument assumes there is no difference between a term in the distributive and collective sense....

-- Fallacy of the four terms -- First-order predicate

First-order predicate

A first-order predicate is a predicate that takes only individual constants or variables as argument. Compare second-order predicate and higher-order predicate.-See also:*First-order predicate calculus...

- First-order predicate calculus - First-order resolution -- Fluidic logic -- Forward chaining

Forward chaining

Forward chaining is one of the two main methods of reasoning when using inference rules and can be described logically as repeated application of modus ponens. Forward chaining is a popular implementation strategy for expert systems, business and production rule systems...

-- Free variables and bound variables

Free variables and bound variables

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place...

-- Fuzzy logic

Fuzzy logic

Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...

H

Heyting algebra

In mathematics, a Heyting algebra, named after Arend Heyting, is a bounded lattice equipped with a binary operation a→b of implication such that ∧a ≤ b, and moreover a→b is the greatest such in the sense that if c∧a ≤ b then c ≤ a→b...

-- Higher-order predicate -- Horn clause

Horn clause

In mathematical logic, a Horn clause is a clause with at most one positive literal. They are named after the logician Alfred Horn, who first pointed out the significance of such clauses in 1951...

-- Hypothetical syllogism

Hypothetical syllogism

In logic, a hypothetical syllogism has two uses. In propositional logic it expresses one of the rules of inference, while in the history of logic, it is a short-hand for the theory of consequence.-Propositional logic:...

I

Iff

IFF

IFF, Iff or iff may refer to:Technology/Science:* Identification friend or foe, an electronic radio-based identification system using transponders...

-- Illicit major

Illicit major

Illicit major is a logical fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion.This fallacy has the following argument form:#All A are B...

-- Illicit minor

Illicit minor

Illicit minor is a logical fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion....

-- Implicant

Implicant

In Boolean logic, an implicant is a "covering" of one or more minterms in a sum of products of a boolean function. Formally, a product term P in a sum of products is an implicant of the Boolean function F if P implies F...

-- Inductive logic -- Inductive logic programming

Inductive logic programming

Inductive logic programming is a subfield of machine learning which uses logic programming as a uniform representation for examples, background knowledge and hypotheses...

-- Inference procedure -- Inference rule -- Infinitary logic

Infinitary logic

An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be compact or complete. Notions of compactness and...

-- Informal logic

Informal logic

Informal logic, intuitively, refers to the principles of logic and logical thought outside of a formal setting. However, perhaps because of the informal in the title, the precise definition of informal logic is matters of some dispute. Ralph H. Johnson and J...

-- Intensional statement

Intensional statement

In logic, an intensional statement-form is a statement-form with at least one instance such that substituting co-extensive expressions into it does not always preserve logical value. An intensional statement is a statement that is an instance of an intensional statement-form. Here co-extensive...

--Interpretability

Interpretability

In mathematical logic, interpretability is a relation between formal theories that expresses the possibility of interpreting or translating one into the other.-Informal definition:Assume T and S are formal theories...

-- Interpretability logic

Interpretability logic

Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability and/or various related metamathematical properties and relations such as weak interpretability, Π1-conservativity, cointerpretability, tolerance, cotolerance and arithmetic...

-- Introduction rule --Intuitionistic linear logic -- Intuitionistic logic

Intuitionistic logic

Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well-formed statements are assumed to be either true or false, even if we do not have a proof of either...

-- Invalid proof

Invalid proof

In mathematics, certain kinds of mistakes in proof, calculation, or derivation are often exhibited, and sometimes collected, as illustrations of the concept of mathematical fallacy...

-- Inverse (logic)

Inverse (logic)

In traditional logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. Any conditional sentence has an inverse: the contrapositive of the converse. The inverse of P \rightarrow Q is thus \neg P \rightarrow \neg Q...

L

language

Language

Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...

-- Lateral thinking

Lateral thinking

Lateral thinking is solving problems through an indirect and creative approach, using reasoning that is not immediately obvious and involving ideas that may not be obtainable by using only traditional step-by-step logic...

-- Law of excluded middle

Law of excluded middle

In logic, the law of excluded middle is the third of the so-called three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is....

-- Law of non-contradiction -- Laws of logic -- Laws of Form

Laws of Form

Laws of Form is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy...

-- Linear logic

Linear logic

Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter...

-- Logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

-- Logic gate

Logic gate

A logic gate is an idealized or physical device implementing a Boolean function, that is, it performs a logical operation on one or more logic inputs and produces a single logic output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and...

-- Logical argument -- Logical assertion

Logical assertion

A logical assertion is a statement that asserts that a certain premise is true, and is useful for statements in proof. It is equivalent to a sequent with an empty antecedent....

-- Logical biconditional

Logical biconditional

In logic and mathematics, the logical biconditional is the logical connective of two statements asserting "p if and only if q", where q is a hypothesis and p is a conclusion...

-- Logical conditional --Logical conjunction

Logical conjunction

In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false....

-- Logical disjunction

Logical disjunction

In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true. E.g. in this context, "A or B" is true if A is true, or if B is true, or if both A and B are...

-- Logical equivalence

Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.Syntactically, p and q are equivalent if each can be proved from the other...

-- Logical fallacy -- Logical language -- Logical nand -- Logical nor

Logical NOR

In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form is true precisely when neither p nor q is true—i.e. when both of p and q are false...

-- Logical operator -- Logicism

Logicism

Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory fathered by Richard Dedekind...

-- Logic programming

Logic programming

Logic programming is, in its broadest sense, the use of mathematical logic for computer programming. In this view of logic programming, which can be traced at least as far back as John McCarthy's [1958] advice-taker proposal, logic is used as a purely declarative representation language, and a...

--logico-linguistic modeling

Logico-linguistic modeling

Logico-linguistic modeling is a method for building knowledge-based systems with a learning capability using Conceptual Models from Soft systems methodology, modal predicate logic and the Prolog artificial intelligence language.- Overview:...

M

Major premise -- Major term

Major term

The major term is the predicate term of the conclusion of a categorical syllogism. It appears in the major premise along with the middle term and not the minor term. It is an end term .Example:...

-- Mathematical logic

Mathematical logic

Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...

-- Mereology

Mereology

In philosophy and mathematical logic, mereology treats parts and the wholes they form...

-- Metalogic

Metalogic

Metalogic is the study of the metatheory of logic. While logic is the study of the manner in which logical systems can be used to decide the correctness of arguments, metalogic studies the properties of the logical systems themselves...

-- Middle term

Middle term

The middle term must distributed in at least one premises but not in the conclusion of a categorical syllogism. The major term and the minor terms, also called the end terms, do appear in the conclusion.Example:...

-- Minimal logic

Minimal logic

Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is a variant of intuitionistic logic that rejects not only the classical law of excluded middle , but also the principle of explosion .Just like intuitionistic logic, minimal logic can be...

-- Minor premise -- Modal logic

Modal logic

Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...

-- Modus ponens

Modus ponens

In classical logic, modus ponendo ponens or implication elimination is a valid, simple argument form. It is related to another valid form of argument, modus tollens. Both Modus Ponens and Modus Tollens can be mistakenly used when proving arguments...

-- Modus tollens

Modus tollens

In classical logic, modus tollens has the following argument form:- Formal notation :...

-- Multi-valued logic

Multi-valued logic

In logic, a many-valued logic is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values for any proposition...

N

Naive set theory

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics , and the everyday usage of set theory concepts in most...

-- Natural deduction

Natural deduction

In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning...

-- Necessary and sufficient -- Negation

Negation

In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...

-- Non-Aristotelian logic

Non-Aristotelian logic

The term non-Aristotelian logic, sometimes shortened to null-A, means any non-classical system of logic which rejects one of Aristotle's premises .-History:...

-- Nonfirstorderizability

Nonfirstorderizability

In formal logic, nonfirstorderizability is the inability of an expression to be adequately captured in particular theories in first-order logic. Nonfirstorderizable sentences are sometimes presented as evidence that first-order logic is not adequate to capture the nuances of meaning in natural...

-- Non-monotonic logic

Non-monotonic logic

A non-monotonic logic is a formal logic whose consequence relation is not monotonic. Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. Intuitively, monotonicity indicates that learning a...

-- Non sequitur (logic)

Non sequitur (logic)

Non sequitur , in formal logic, is an argument in which its conclusion does not follow from its premises. In a non sequitur, the conclusion could be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion. All formal fallacies...

P

Paraconsistent logics -- Paradox

Paradox

Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

-- Pierce's law -- Plural quantification

Plural quantification

In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London etc...

--Polish notation

Polish notation

Polish notation, also known as prefix notation, is a form of notation for logic, arithmetic, and algebra. Its distinguishing feature is that it places operators to the left of their operands. If the arity of the operators is fixed, the result is a syntax lacking parentheses or other brackets that...

-- Polysyllogism

Polysyllogism

A polysyllogism is a string of any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on...

--Predicate -- Principia Mathematica

Principia Mathematica

The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913...

-- Principle of bivalence

Principle of bivalence

In logic, the semantic principle of bivalence states that every declarative sentence expressing a proposition has exactly one truth value, either true or false...

-- Proof theory

Proof theory

Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...

-- Proposition

Proposition

In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

-- Propositional calculus

Propositional calculus

In mathematical logic, a propositional calculus or logic is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true...

-- Provability logic

Provability logic

Provability logic is a modal logic, in which the box operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic....

S

Satisfiability -- Scholastic logic -- Second-order predicate

Second-order predicate

In mathematical logic, a second-order predicate is a predicate that takes a first-order predicate as an argument. Compare higher-order predicate....

-- Self-reference

Self-reference

Self-reference occurs in natural or formal languages when a sentence or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding...

-- Sequent

Sequent

In proof theory, a sequent is a formalized statement of provability that is frequently used when specifying calculi for deduction. In the sequent calculus, the name sequent is used for the construct which can be regarded as a specific kind of judgment, characteristic to this deduction system.-...

-- Sequent calculus

Sequent calculus

In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi, systems LK and LJ, were introduced by Gerhard Gentzen in 1934 as a tool for studying natural deduction in...

-- Sequential logic

Sequential logic

In digital circuit theory, sequential logic is a type of logic circuit whose output depends not only on the present input but also on the history of the input. This is in contrast to combinational logic, whose output is a function of, and only of, the present input...

-- Singular term

Singular term

There is no really adequate definition of singular term. Here are some definitions proposed by different writers:# A term that tells us which individual is being talked about....

-- Soundness

Soundness

In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formulas that are valid with respect to its semantics. In most cases, this comes down to its rules having the property of preserving truth, but this is not the case in general. The word...

-- Square of opposition

Square of opposition

In the system of Aristotelian logic, the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related to each of the others...

-- Strict conditional

Strict conditional

In logic, a strict conditional is a material conditional that is acted upon by the necessity operator from modal logic. For any two propositions p and q, the formula p \rightarrow q says that p materially implies q while \Box says that p strictly implies q...

-- Strict implication -- Strict logic

Strict logic

Strict logic is essentially synonymous with relevant logic, though it can be characterized proof-theoretically as* ordinary logic without weakening, or* linear logic with contraction....

-- Structural rule

Structural rule

In proof theory, a structural rule is an inference rule that does not refer to any logical connective, but instead operates on the judgements or sequents directly. Structural rules often mimic intended meta-theoretic properties of the logic...

-- Sufficient condition -- Syllogism

Syllogism

A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

-- Syllogistic fallacy

Syllogistic fallacy

Syllogistic fallacies are logical fallacies that occur in syllogisms. They include:Any syllogism type :*fallacy of four termsOccurring in categorical syllogisms:*related to affirmative or negative premises:...

T

Tautology

Tautology (logic)

In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...

-- Temporal logic

Temporal logic

In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. In a temporal logic we can then express statements like "I am always hungry", "I will eventually be hungry", or "I will be hungry...

-- Term -- Term logic

Term logic

In philosophy, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century...

-- Ternary logic

Ternary logic

In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value...

-- Theorem

Theorem

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...

-- Tolerance -- Trilemma

Trilemma

A trilemma is a difficult choice from three options, each of which is unacceptable or unfavourable.There are two logically equivalent ways in which to express a trilemma: it can be expressed as a choice among three unfavourable options, one of which must be chosen, or as a choice among three...

--Truth

Truth

Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...

-- Truth condition

Truth condition

In semantics, truth conditions are what obtain precisely when a sentence is true. For example, "It is snowing in Nebraska" is true precisely when it is snowing in Nebraska....

-- Truth function -- Truth value -- Type theory

Type theory

In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...