# Web-Based Assessment System Applying Many-Valued Logic

Sylvia Encheva (Haugesund University College, Norway) and Sharil Tumin (University of Bergen, Norway)
DOI: 10.4018/978-1-59904-849-9.ch236

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## Background

A brief overview of a six-valued logic, which is a generalized Kleene’s logic (Kleene, S., 1952), has been first presented by Moussavi, M. & Garcia, N., 1989. Fitting, 1991 developed further this logic by assigning probability estimates to formulas instead of non-classical truth values.

The six-valued logic distinguishes two types of unknown knowledge values - permanently or eternally unknown value and a value representing current lack of knowledge about a state (Garcia, O.N. & Moussavi, M., 1990).

Two kinds of negation, weak and strong negation are discussed in Wagner, G., 1994. Weak negation or negation-as-failure refers to cases when it cannot be proved that a sentence is true. Strong negation or constructable falsity is used when the falsity of a sentence is directly established.

The semantic characterization of a four-valued logic for expressing practical deductive processes is presented by Belnap N.J., 1977. In Gurfinkel, A. & Chechik, M. 2005, it is shown that additional reasoning power can be obtained without sacrificing performance, by building a prototype software model-checker using Belnap’s logic.

Bi-dimensional systems representing and reasoning with temporal and uncertainty information have appeared also in Felix, P., Fraga, S., Marin, R., & Barro, S., 1999, and Mulsliner, D.J., Durfee, E.H., Shin, K.G., 1993.

## Key Terms in this Chapter

Belnap’s Logic: It has four truth values ‘T, F, Both, None’. The meaning of these values can be described as follows: an atomic sentence is stated to be true only (T), an atomic sentence is stated to be false only (F), an atomic sentence is stated to be both true and false, for instance, by different sources, or in different points of time (Both), and an atomic sentences status is unknown. That is, neither true, nor false (None).

XML-RPC: It is remote procedure calling using HTTP as the transport and XML as the encoding.

Six-Valued Logic: The six-valued logic obtained as an extension of the Kleene’s logic has six truth values - true, false, unknown, unknownt - intermediate level of truth between unknown and true, unknownf - intermediate level of truth between unknown and false, contradiction.

Lukasiewicz’s Generalized Logic: It is done by inserting evenly spaced division points in the interval between 0 and 1.

Kleene’s Logic: Kleene’s logic has three truth values, truth, unknown and false, where unknown indicates a state of partial vagueness. These truth values represent the states of a world that does not change.

LAMP Web Server: It is a combination of free software tools of an Apache Web server, a database server and a scripting programming platform on a Linux operating environment. Lukasiewicz’s Three-Valued Logic: Lukasiewicz’s three-valued valued logic has a third value, 1/2, attached to propositions referring to future contingencies. The third truth value can be construed as ‘intermediate’ or ‘neutral’ or ‘indeterminate’.

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