1. General Logic-Systems and Consequence Operators - Herrmann, Robert A.
It is shown that thereare infinitely many finite consequence operators defined on a fixed language Lthat cannot be generated from a finite logic-system.

2. Practical Methods for Proving Termination of General Logic Programs - Marchiori, E.
Termination of logic programs with negated body atoms (here called generallogic programs) is an important topic.

3. A Dynamic Approach to Characterizing Termination of General Logic Programs - Shen, Yi-Dong; You, Jia-Huai; Yuan, Li-Yan; Shen, Samuel S. P.; Yang, Qiang
We proposea dynamic approach which employs some key dynamic features of an infinite(generalized) SLDNF-derivation, such as repetition of selected subgoals andrecursive increase in term size.

4. Alethic -- from MathWorld - Weisstein, Eric W.
A term in logic meaning pertaining to truth and falsehood.

5. Analogy -- from MathWorld - Weisstein, Eric W.
In the hands of a skilled mathematician, analogy can be a very powerful tool for suggesting new and extending old results.

6. Atomic Statement -- from MathWorld - Weisstein, Eric W.
In logic, a statement which cannot be broken down into smaller statements, also simply called an "atom.".

7. Axiom Schema -- from MathWorld - Weisstein, Eric W.
Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference rules.

8. Bivalent -- from MathWorld - Weisstein, Eric W.
See also: Law of the Excluded Middle, Univalent.

9. Boolean Connective -- from MathWorld - Weisstein, Eric W.
One of the logic operators AND \land, OR \lor, and NOT \lnot.

10. Bound Variable -- from MathWorld - Weisstein, Eric W.
Bound variables are also called dummy variables.

11. Caliban Puzzle -- from MathWorld - Weisstein, Eric W.
A puzzle in logic in which one or more facts must be inferred from a set of given facts.

12. Church-Rosser Property -- from MathWorld - Weisstein, Eric W.
A reduction system is said to posses the Church-Rosser property if, for all x and y such that x \leftrightarrow_* y, there exists a z such that x\to_* z and y\to_* z.

13. Church-Rosser Theorem -- from MathWorld - Weisstein, Eric W.
The Church-Rosser theorem states that lambda calculus as a reduction system with lambda conversion rules satisfies the Church-Rosser property.

14. Clause -- from MathWorld - Weisstein, Eric W.
A clause is a disjunction of literals.

15. Closed Sentential Formula -- from MathWorld - Weisstein, Eric W.
Examples of closed sentential formulas are given by \forall x\forall y(x+y \equiv y+x), which expresses the commutativity of addition, and \forall x \exists y(\forall u \forall v (x + y \not= (u+2)(v+2))), which expresses the infinitude of the primes.

16. Combinator -- from MathWorld - Weisstein, Eric W.
Schönfinkel presented a report to the Mathematical Society in Göttingen a new type of formal logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924).

17. Combinatory Logic -- from MathWorld - Weisstein, Eric W.
A fundamental system of logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924).

18. Conclusion -- from MathWorld - Weisstein, Eric W.
A conclusion is a statement arrived at by applying a set of logical rules known as syllogisms to a set of premises.

19. Conjunctive Normal Form -- from MathWorld - Weisstein, Eric W.
Examples of conjunctive normal forms include A (1) (A\lor B)\land({!A}\lor C) (2) (A\lor B\lor {!A})\land(C\lor {!B})\land(A\lor {!C}) (3) A\lor B (4) A\land(B\lor C), (5) where \lor denotes OR, \land denotes AND, and .

20. Consistency -- from MathWorld - Weisstein, Eric W.
The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

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