This glossary is designed to give the reader partial inderstanding of how certain terms are used in the study of logic. It is not designed to give either very detailed or complete information. For that, one must consult appropriate logic texts. A short bibliography is included at the end.

• Acceptable argument: An argument that is taken to have true premises which lead to a conclusion either conclusively or with a high degree of probably. An argument that could lead one to action.
• Accident: An informal fallacy occurring when one applies a general rule incorrectly to a specific case or in a specific situation.
• Antecedent: The component in conditional sentences that implied the consequent. Example: 'A' is the antecedent in '(A & B)'. The ampersand used here ('&') is used in place of a "dot," which looks like the period at the end of a sentence, but in logic we put the dot on the middle of the line.
• Argument: A series of sentences, one of which is intended to follow from the other(s) either conclusively or with a high degree of probability.
• Argumentum ad Baculum: An informal fallacy occurring when one person threatens another person in order to persuade the second person to accept some conclusion.
• Argumentum ad Hominem/Abusive: An argument directed toward a person in which the arguer attacks the character of the person in an abusive manner. An informal fallacy.
• Argumentum ad Hominem/Circumstantial: An argument directed toward a person in which the arguer attacks the person by pointing out the special situation the person is in. An informal fallacy.
• Argumentum ad Hominem/Tu Quoque: An argument directed toward a person in which the arguer accuses the person of having said or done something similar to what the arguer allegedly said or did. An informal fallacy.
• Argumentum ad Ignorantiam: An informal fallacy occurring when one states that nothing is or can be known about some object and then states something that is known about the object.
• Argumentum ad Misericordiam: An informal fallacy occurring when one appeals to a listener's feeling of pity for some person(s) in order to get the listener to accept some conclusion or other.
• Argumentum ad Populum: An informal fallacy occurring when one appeals to a listener's desire or need to be 'one of the group' to get the listener to accept some conclusion or other.
• Argumentum ad Vericundiam: An informal fallacy occurring when one appeals exclusively to the authority of a person to get some conclusion or other accepted.
• Arrow: Logical symbol used to designate conditional sentences. Example: (A --> B).
• Bar: Logical symbol used to designate negative sentences. Examples: -A, -(A v B).
• Begging the question: See Petitio Principii.
• Biconditional sentence: A compound sentence in which the components are said to imply one another. Example: The Yankees will win if, and only if, they play the Orioles. The logical symbolism makes use of the double arrow and looks like this: (Y <--> O). What this sentence says is that if the Yankees play the Orioles, then the Yankees will win and if the Yankees win, then they will play the Orioles.
• Categorical sentence: A sentence composed of a quantifier (All/No/Some), a subject term (S), a copula (any form of the verb 'to be'), and a predicate term (P). Examples: All S are P; No S are P; Some S are P; Some S are not P.
• Categorical syllogism: An argument consisting of three categorical sentences in normal form.
• Checked formula/sentence: In truth trees, a sentence to which a rule has been applied.
• Closed branch: In truth trees, a closed branch is a branch on which there exists an explicit contradiction.
• Composition: An informal fallacy occurring when one argues that because something is true of the parts of some whole it is therefore also true of the whole itself.
• Compound sentence: A sentence consisting in two or more simple sentences.
• Conclusion: The sentence in an argument that is supposed to follow from a number of other sentences, called the premises.
• Conclusion indicator: A word or phrase, e.g., 'hence', marking the presence of the conclusion in an argument.
• Conditional sentence: A compount sentence in which one sentence is said to imply or entail another sentence.
• Conjunct: A component sentence in a conjunction. Example: 'A' and 'B' are conjuncts in '(A & B)'.
• Conjunction: (Conjunctive Sentence) A compound sentence in which it is asserted that both components are true. Example: The Yankees lost their game and Yogi Berra hit two home runs.
• Consequent: The component in conditional sentences that is implied by the antecedent. Examples: 'it will rain' is the consequent in 'If the wind blows from the north, then it will rain'; 'B' is the consequent in
  '(A --> B)'.
• Contradictory sentences: Two sentences are contradictory if and only if they have opposite truth values under all interpretations. Contradictory sentences cannot both be true at the same time and cannot both be false at the same time. Examples: '(A . B)' and '-(A . B)' are contradictories, as are 'All musicians listen to the Beatles' and 'Some musicians do not listen to the Beatles'.
• Contradiction: A contradiction is commited either when one asserts a logically false sentence or when one asserts any sentence and its negation as both true or both false.
• Contraries: A relation holding between 'A' and 'E' sentences in Aristotelian Logic. Contraries cannot both be true at the same time but may both be false at the same time.
• Contraposition: A method of inference in Aristotelian Logic holding for 'A' and 'O' sentences whereby the subject term is replaced by the negation of the predicate term and the predicate term is replaced by the negation of the subject term. Also, a Principle of Replacement in Natural Deduction whereby the antecedent in a conditional is replaced by the negation of the consequent and the consequent is replaced by the negation of the antecedent.
• Conversion: A method of inference in Aristotelian Logic holding for 'E' and 'I' sentences whereby the subject and predicate terms are exchanged.
• Copula: A form of the verb 'to be' positioned between the subject and predicate terms in normal form categorical sentences, usually 'are' or 'are not'.
• Counterexample: An argument designed to show the invalidity of a different argument by having the precise form of the other argument, but which has true premises and a false conclusion.
• Deontic fallacy: An informal fallacy occurring when one draws a a conclusion which is prescriptive in nature based only on descriptive statements as premises.
• Disjunct: The component sentences in disjunctions. Example: 'A' and 'B' are disjuncts in '(A v B)'.
• Disjunction: (Disjunctive sentence) A sentence in which it is asserted that one or the other of two sentences is true. Example: 'Either the Yankees will win or the owners will be mad'.
• Division: An informal fallacy occurring when one argues that because something is true of the whole of some object it is also true of the parts of the whole.
• Distributed term: A term is said to be distributed in a normal form categorical sentence if the sentence refers to every member of the class dsignated by the term.
• Dot: Logical symbol used to designate conjunctions. Example: (A & B).
• Double arrow: Logical symbol used to designate biconditionals. Example: (A <--> B).
• Equivalent sentences: Two sentences are said to be equivalent if and only if they are true under the same interpretations and false under the same interpretations. Example: (A --> B) and (-A v B) are equivalent.
• Equivocation: An informal fallacy occurring when one uses a word or phrase in two or more senses (meanings) within the same sentence/paragraph/context.
• Existential quantifier: The logical symbol designated by words and phrases such as 'some' and 'a few'. The logician takes its literal meaning to be 'there exists at least one'. The symbolic representation for 'there exists at least one x' is '(Ex)'. (The 'E' you see there should be turned around.)
• False cause: An informal fallacy occurring when one draws a conclusion on the basis of an erroneous causal relationship.
• Figure: One of four forms of placement of the middle term in a normal form categorical syllogism.
• Hasty generalization: An informal fallacy occurring when one argues to a generalization on the basis either of atypical cases or an insufficient number of cases.
• Ignoratio Elenchi: An informal fallacy occurring when a different conclusion is drawn from a set of premises rather than the expected conclusion.
• Incompatible sentences: Sentences that have the same truth values under some interpretations and different truth values under other interpretations. Example: (A v B) and (A & B) are incompatible sentences.
• Individual constant: See 'Name Letter'.
• Instantiation: The process of replacing instances of variables with individual constants. Example: (Ai v Bi) is an instantiation of (x)(Ax v Bx).
• Interpretation: Each row in a truth table, each branch in a truth tree, and each instantiation, is considered an interpretation.
• Invalid argument: An argument in which it is possible for the premises to be true and the conclusion false.
• Law of Excluded Middle: The 'law of thought' expressinf the facxt that every sentence is either true or false and that no sentence is both true and false.
• Limited alternative: An informal fallacy occurring when an aruer suggests/presents a lesser number of [obvious] alternatives than there actually are.
• Logic: The study of correct and incorrect reasoning.
• Logically false sentence: A sentence that is true under no interpretations. Example: (A & -A).
• Logically indeterminate sentence: A sentence that is true under some but not all interpretations. A sentence which is neither logically true nor logically false.
  Example: (A v B).
• Logically true sentence: A sentence that is true under all interpretations. Example: (A v -A). also called a Tautology.
• Major premise: The premise in a normal form categorical syllogism containing the major term.
• Major term: The predicate term in the conclusion of a normal form categorical syllogism.
• Middle term: The term which appears once in each premise of a normal form categorical syllogism.
• Minor premise: The premise in a normal form categorical syllogism containing the minor term.
• Minor term: The subject term in the conclusion of a normal form categorical syllogism.
• Mood: A designation, using A, E, I, and O, of the type of sentences comprising normal form categorical sentences and syllogisms, in the following order: major premise, minor premise, conclusion.
• Name letter: The logical symbol (a lower case letter from 'a' to 'o') representing an individual or constant, e.g., 'a' in 'Ra'.
• Necessary Condition: In a conditional sentence, the necessary condition is represented by the consequent. Example: In '(A --> B)', 'B' is the consequent, hence a necessary ondition for 'A'.
• Obversion: A method of inference in Aristotelian Logic holding for A, E, I, and O sentences whereby the quality of the sentence is changed from affirmative to negative, or vice-versa, and the predicate term is negated.
• Open branch: In truth trees, an open branch is a branch that does not contain a contradiction when all formulas on the branch that can be checked have been checked.
• Particular Affirmative sentence: A categorical sentence of the form 'Some S are P'. An I sentence in Aristotelian Logic.
• Particular Negative sentence: A categorical sentence of the form 'Some S are not P'. An O sentence in Aristotelian Logic.
• Petitio Principii: Also named Begging the Question. A fallacy occurring when one assumes the very conclusion for which one is arguing. Alternatively, also occurring when one fails to make explicit a premise that is at the heart (usually very controversial) of the issue/point about which one is arguing. Further, anytime one assumes a controversial point without argument begs the question.
• Predicate: In symbolic logic, 'R' in 'Ra' is the predicate. In natural language, the predicate indicates what is said about an individual or object, e.g., "Rachel is an architect", in which 'is an architect' is the predicate.
• Predicate letter: In symbolic logic, the symbol (an upper case letter) which represents the predicate, e.g., 'R' in 'Ra'.
• Predicate term: The word or phrase directly following the copula in a normal form categorical sentence.
• Premise(s): The sentence(s) in an argument designed to provide support for a further sentence, called the conclusion.
• Premise indicator: A word or phrase, e.g., since, marking the presence of a premise in an argument.
• Primary connective: In a symbolized sentence the primary connective is the connective with the widest scope, i.e., ranges over all other symbols in the sentence. Example: In '[(A v B) --> C]' the arrow is the primary connective.
• Proof: A demonstration of the validity of an argument in Natural Deduction.
• Quantifier: A word, phrase, or logical symbol in a sentence that indicates the quantity of class membership.
• Quantifier Exchange: The process of replacing one quantifier form with another, equivalent, quantifier form. Example: '-(x)Rx' can replace or be replaced by '(Ex)-Rx'.
• RAA: Abbreviation for Reductio ad Absurdum
• RCP: Abbreviation for 'Rule of Conditional Proof'.
• Reductio ad Absurdum: A method of determining validity in which one assumes the conclusion to be false and attempts to derive a contradiction using the premises in conjunction with the denied conclusion. Alternatively, a rule stating that if the conclusion of a given argument is assumed to be false and a contradiction results, then the original argument is valid. Also called Indirect Proof.
• Rule of Conditional Proof: In Natural Deduction, the use of a rule whereby one assumes any sentence ( ), derives another sentence ( ) through a finite number of applications of the rules of inference and/or principles of replacement, then closes the scope of the assumption, after which a further sentence ( ) is derived, in the form of a conditional in which is the antecedent and is the consequent.
• Self-contradiction: A logically false sentence.
• Simple sentence: In sentential logic, a sentence expressing essentially one idea. Example: The leaves are brown.
• Sound argument: A sound argument is one that is valid and has true premises.
• Subalternation: A relation existing between A and I and between E and O sentences in Aristotelian Logic, where the first of these pairs implies the second in the pair. See the Traditional Square of Opposition.
• Subcontraries: A relation holding between I and O sentences in Aristotelian Logic. Subcontraries can both be true at the same time but cannot both be false at the same time.
• Subject term: The class term or phrase directly following the quantifier in a normal form categorical sentence.
• Subordinate connective: Any connective in a symbolized sentence that is not the primary connective. Example: In '[(A v B) --> -C]' both the wedge and the bar are subordinate connectives. The arrow is the primary connective.
• Sufficient condition: In a conditional sentence, the sufficient is represented by the antecedent.
• Tautology: A logically true sentence.
• Traditional Square of Opposition: A diagram indicating the various relationships holding between normal form categorical sentences in Aristotelian Logic.
• Translation: A replacement of a sentence in natural language, e.g., English, with a sentence in symbolic notation.
• Translation dictionary: A dictionary for sentence letters used in translating sentences from natural to artificial language.
• Truth functional connective: The words or phrases, e.g., and/or/if and only if, connecting the simple sentences in conjunctions, conditionals, disjunctions, and biconditionals. In symbolic form, the truth functional connectives are represented by the arrow, dot wedge, bar and double arrow.
• Truth table: A method by which arguments are shown to be valid or invalid and by which sentences are shown to be logically true, logically false, or logically indeterminate.
• Truth tree: A method by which arguments are shown to be valid or invalid and by which sentences are shown to be logically true, logically false, or logically indeterminate.
• Truth value: In truth functional logic (sentential logic), which is a two-valued system, the values are 'truth' and 'falsehood'. In truth tables, we assign 't' for true (truth) and 'f' for false (falsehood). A sentence has the truth value 'true' if the sentence is true and has the value 'false' if it is false.
• Univsersal Affirmative sentence: A categorical sentence of the form 'All S are P'. An A sentence in Aristotelian Logic.
• Universal Negative sentence: A categorical sentence of the form 'No S are P'. An E sentence in Aristotelian Logic.
• Universal quantifier: The universal quantifier is designated by words and phrases such as 'all', 'every', 'each', 'no', 'none'. The symbolic representation is '(x)'.
• Valid argument: An argument in which it is impossible for the premises to be true while the conclusion is false.
• Variable: In symbolic logic, a letter (e.g., x, y, z) used as a placeholder for individual constants. Example: (x)Ax.
• Venn Diagram: For categorical sentences: Two overlapping circles, each representing a class of individuals or objects, which are marked to indicate class inclusion or class exclusion. (2) For categorical syllogisms: Three overlapping circles, each representing a class of individuals or objects, which are mrked to indicate class inclusion or class exclusion. Venn diagrams were created bvy John Venn, a 19th century mathematician/logician.
• Wedge: Also known as the 'vee' or the 'vel'. Logical symbol ('v') used to designate disjunctions.
  Example: '(A v B)'.