# Deductive Logic Calculus

A Deductive Logic Calculus is a logic system with a finite set of allowable deductive logic operations that can form necessary conclusions.

**AKA:**Deductive Theory.**Context:**- It can include a Deductive Logic Language.
- It can support a Deductive Argument.
- It can range from being a Monotonic Logic System to being a Non-Monotonic Logic System.

**Example(s):**- Boolean Logic System.
- Propositional Logic System.
- Axiomatic Deductive Logic Framework (axiomatic system).
- a Predicate Logic System.
- …

**Counter-Example(s):****See:**Deductive Reasoning, Axiomatic Deductive Logic System.

## References

### 2013

- (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Deductive_system
- A
**deductive system**(also called a deductive apparatus of a formal system) consists of the axioms (or axiom schemata) and rules of inference that can be used to derive the theorems of the system.^{[1]}Such a deductive system is intended to preserve deductive qualities in the formulas that are expressed in the system. Usually the quality we are concerned with is truth as opposed to falsehood. However, other modalities, such as justification or belief may be preserved instead.

In order to sustain its deductive integrity, a

*deductive apparatus*must be definable without reference to any intended interpretation of the language. The aim is to ensure that each line of a derivation is merely a syntactic consequence of the lines that precede it. There should be no element of any interpretation of the language that gets involved with the deductive nature of the system.

- A

- ↑ Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971

### 1997

- (Either et al, 1997) ⇒ Thomas Eiter, Nicola Leone, Cristinel Mateis, Gerald Pfeifer, and Francesco Scarcello. (1997). “A Deductive System for Non-Monotonic Reasoning.” In: Logic Programming and Nonmonotonic Reasoning.

### 1994

- (Ramakrishnan et al, 194) ⇒ Raghu Ramakrishnan, Divesh Srivastava, S. Sudarshan, and Praveen Seshadri. (1994). “The CORAL deductive system." The VLDB Journal, 3(2).
- (Gabbay, 1994) ⇒ Dov M. Gabbay. (1994). “What is a logical system?."