This page gathers the 457 dictionary entries belonging to the domain “Logic”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples. Page 2 of 5: from “contrary” to “Herbrandization”.
- contrary noun One of a pair of propositions that cannot both be simultaneously true, though they may both be false.
- converse noun Of a proposition or theorem consisting of a statement of the form "If A is true, then B is true", the statement "If B is true, then A is…
- conversion noun The act of interchanging the terms of a proposition, as by putting the subject in the place of the predicate, or vice versa.
- convert verb To change (one proposition) into another, so that what was the subject of the first becomes the predicate of the second.
- convertend noun Any proposition which is subject to the process of conversion; so called in its relation to itself as converted, after which process it is…
- convertible adj Able to undergo conversion (i.e., inversion) without falsehood.
- corollary noun A proposition which follows easily from the statement or proof of another proposition.
- counterexample noun An example that counters a general rule; an exception to a general rule; a specific instance of the falsity of (and falsifiability of) any…
- counterextension noun The set of tuples of values that, used as arguments, do not satisfy the predicate.
- counterlegal adj That goes against a system of laws, such as the laws of nature.
- counterproof noun A proof that contradicts a given statement.
- crocodile noun A fallacious dilemma, mythically supposed to have been first used by a crocodile.
- cum hoc ergo propter hoc noun The logical fallacy of assuming that two events that occur at the same time have a cause-and-effect relationship.
- De Morgan's law noun The negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ 𝑞) ⇔ (¬ 𝑝) ∨ (¬ 𝑞)
- decidable adj in intuitionistic logic, a proposition P is decidable in a given theory if it can be proven from the theory that "either P or not P", i.e.…
- deduction noun A conclusion; that which is deduced, concluded or figured out.
- deduction theorem noun A procedure for "discharging" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa.…
- deductive adj Based on inferences from general principles.
- deep embedding noun The act of representing one language, typically a logic or programming language, with another by modeling expressions in the former as data…
- defeater noun a belief which, if proved to be true, would imply outright or indirectly that another belief were false.
- definitive description noun A phrase that designates an object by providing a description that is satisfied by exactly one object.
- deflationary adj Belonging or relating to a family of theories claiming that assertions that predicate truth of a statement do not attribute a property…
- degree noun The number of logical connectives in a formula.
- denial noun The negation in logic.
- denotation noun The primary, surface, literal, or explicit meaning of a signifier such as a word, phrase, or symbol; that which a word denotes, as…
- deontic logic noun The study of obligation, permission, and related concepts.
- depth noun the number of simple elements which an abstract conception or notion includes; the comprehension or content
- derive verb To deduce (a conclusion) by reasoning.
- description logic noun One of a family of knowledge representation languages which can be used to represent the concept definitions of an application domain…
- desitive noun An argument that leads to a conclusion.
- destructive sorites noun A form of reductio ad absurdum which involves the denial of the first of a series of dependent propositions as a consequence of the denial…
- determine verb To define or limit by adding a differentia.
- dialetheism noun The theory that statements can be both true and false at the same time and in the same sense. The opposite of the law of noncontradiction.
- dichotomy noun The division of a class into two disjoint subclasses that are together comprehensive, as the division of human into female and male.
- difference noun The quality or attribute which is added to those of the genus to constitute a species; a differentia.
- dilemma noun A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D…
- direct adj Not employing the law of the excluded middle or argument by contradiction.
- dirimens copulatio noun Mentioning a balancing or opposing fact to prevent the argument from being one-sided or unqualified.
- discharge verb To release (an auxiliary assumption) from the list of assumptions used in arguments, and return to the main argument.
- discretive noun A discretive proposition.
- discretive proposition noun A compound proposition in which contrasting judgments are made, connected by a word such as "but" or "though".
- disjunct noun One of multiple propositions, any of which, if true, confirm the validity of another proposition (a disjunction).
- disjunction noun The proposition resulting from the combination of two or more propositions using the or operator.
- disjunctive noun A disjunction.
- disjunctive normal form noun The form of a boolean formula that the formula has if the formula is a disjunction of conjunctions of literals, such as “(A and B and C) or…
- disjunctive syllogism noun A logical argument of the form that if there are only two possibilities, and one of them is ruled out, then the other must take place. In…
- distribute verb To employ (a term) in its whole extent; to take as universal in one premise.
- distribution noun The resolution of a whole into its parts.
- distributive adj Assigning the species of a general term.
- DM noun Initialism of De Morgan’s law.
- domain of discourse noun In predicate logic, an indication of the relevant set of entities that are being dealt with by quantifiers.
- dormitive principle noun A type of tautology in which an item is explained in terms of the item itself, only put in different (usually more abstract) words.
- dormitive virtue noun A type of tautology in which an item is explained in terms of the item itself, only put in different (usually more abstract) words.
- double turnstile noun The ⊨ symbol used to denote semantic consequence, or the ⊧ symbol used to denote the fact that the model to the left of it satisfies the…
- double-barreled question noun an informal fallacy. It is committed when someone asks a question that touches upon more than one issue, yet allows only for one answer.
- dyadic adj having an arity of two (taking two arguments or operands)
- ecthesis noun An exposition or setting out; used by Aristotle in setting forth various proofs, though the nature of the process is disputed; perhaps…
- elementary equivalence noun A relation between two structures which have the property that every first-order formula is valid in one structure if and only if it is…
- elench noun That part of an argument on which its conclusiveness depends; that which convinces or refutes an antagonist; a refutation.
- elimination noun The act of obtaining by separation, or as the result of eliminating; deduction.
- enthymeme noun A syllogism with a required but unstated assumption.
- Entscheidungsproblem noun A decision problem of finding a way to decide whether a formula is true or provable within a given system.
- epagoge noun The adducing of particular examples so as to lead to a universal conclusion; the argument by induction.
- epichirema noun A syllogism in which the proof of the major or minor premise, or both, is introduced with the premises themselves, and the conclusion is…
- epichireme noun A dialectical inference; a syllogism based on probable premises (endoxa), as opposed to a philosopheme which is a demonstrative or…
- episyllogism noun A syllogism which assumes as one of its premises a proposition which was the conclusion of a preceding syllogism (the prosyllogism).
- equipollence noun Sameness of signification of two or more propositions which differ in language.
- equipollent adj able to be deduced from the other
- equiprobable adj Having equal probability, such as any number from 1 to 6 being the equiprobable outcome of the fair toss of fair dice.
- equisatisfiable adj Of a pair of formulas, where one formula is satisfiable whenever the other is satisfiable (either both formulas are satisfiable or both are…
- equivalence noun The relationship between two propositions that are either both true or both false.
- equivocation noun A logical fallacy resulting from the use of multiple meanings of a single expression.
- exclusive or noun Exclusive disjunction: the use of or to indicate that of two predicates, one is true and one is false (without specifying which is which)…
- existential adj Of or relating to existence.
- existential instantiation noun In predicate logic, an inference rule of the form ∃x P(x) ⊢ P(c), where c is a new symbol (not part of the original domain of discourse…
- existential quantifier noun The operator, represented by the symbol ∃, used in predicate calculus to indicate that a predicate is true for at least one member of a…
- exportation noun Either the logical law ((P∧Q)→R)⇒(P→(Q→R)), or the rule of replacement ((P∧Q)→R)⇔(P→(Q→R)).
- extension noun The set of tuples of values that, used as arguments, satisfy the predicate.
- factored adj Expressed in terms of factors (values that are multiplied together to form a whole)
- fallacy noun An argument, or apparent argument, which professes to be decisive of the matter at issue, while in reality it is not; a specious argument.
- fallacy fallacy noun The formal fallacy of inferring that if an argument contains a fallacy, its conclusion must be false.
- false adj Of a state in Boolean logic that indicates a negative result.
- false analogy noun An informal fallacy applying to inductive arguments, in which the similarity in one respect of two concepts, objects, or events is taken as…
- false cause noun The fallacy of stating as a cause what is not actually the cause; the fallacy of non causa pro causa.
- figure noun The form of a syllogism with respect to the relative position of the middle term.
- finitary adj Pertaining to finite-length proofs, each using a finite set of axioms.
- first-order adj Of one of a series of models, languages, relationship, forms of logical discourse, etc., being the simplest one or the first in a sequence.
- first-order logic noun A formal deductive system extended from propositional logic with the possibility to quantify over individuals of the domain of discourse.
- for prep Used to introduce a variable subject to quantification, or to establish a restricting domain for a subsequent mathematical statement.
- formal logic noun Mathematical logic.
- formula noun A syntactic expression of a proposition, built up from quantifiers, logical connectives, variables, relation and operation symbols, and…
- free adj Unconstrained by quantifiers.
- free variable noun A variable (occurring within some expression or well-formed formula) which is not bound by a quantifier or analogous symbol (such as a…
- fuzzy math noun A form of logic based on the concept of a fuzzy set.
- Gödel sentence noun An arithmetic statement that can be metatheoretically shown to not be provable or refutable in a formal system.
- graphoid noun A set of statements of the form, "X is irrelevant to Y given that we know Z" where X, Y and Z are sets of variables, which can be…
- guilt by association noun A fallacy where a person or idea is judged guilty or discredited solely due to their connection to someone or something that is viewed…
- Herbrand function noun A function which replaces a variable bound by a universal quantifier which lies in the scope of an even number of logical negations; such…
- Herbrand universe noun The set of all ground terms that may be formed (even recursively) using any of the constants and functions which appear in a given set of…
- Herbrandization noun The conversion of a formula of first-order logic which involves the following steps: (1) replace free variables with constants, (2) replace…