Multi-valued logic

In this paper we describe the need for planning, and then develop the predicate calculus we used and the choice of multi-valued logic. Finally we briefly describe the QED program, a few rules, and an example analysis. Other papers in the QED series will cover the program and chemical results in detail. 

In summary, the value of an implication rule is an inverse measure of how often the antecedent has a higher value than the consequent. This is very important in multi-valued logics where the truth value ranges over many numbers rather than just 0 and 1. The more "valuable" the rule, the more often it implies the correct consequence. 

The method for calculating tb is exactly that described in the introduction to this chapter for binary and multi-valued logic. The process is one of calculating fuzzy truth restrictions for the first and second lines of the deduction on the space Ux X Uy, intersecting them to produce an equivalent restriction and then projecting the result on to Uy Thus... 

An exponent of the traditional multi-valued logical system is the technique introduced by Lukasiewicz in the 1920s, which is introduced, for example, in Lukasiewicz (1935 176). For the contribution of Lukasiewicz s work to temporal logic refer to Ohrstrom Hasle (1995 149). 

The multi-valued predicate calculus logic as implemented in QED has been demonstrated to be suitable for cleanly representing strategic axioms of chemical synthesis. QED is a powerful tool for exploring inference in the planning of synthesis strategies. QED helped us elucidate key strategic concepts and their interdependence and... 

The tolerance of the fuzzy in the process of human rezoning suggests that most of the logic behind the human rezoning is not the traditional bi-valued logic, or even the multi-valued, but the logic with fuzzy values, with fuzzy connections and fuzzy rules or inferences. 

Zaitseva, E. 2003. Dynamic Reliability Indices for Multi-State System. Proc of the IEEE 33th Int. Symp on Multiple-Valued Logic, Tokyo, Japan 287-292. 

Zaitseva, E. 2012. Importance analysis of a multi-state system based on multiple-valued logic methods. In Lisnianski A. and Frenkel I. (eds) Recent Advances in System Reliability Signatures, Multi-state Systems and Statistical Inference London Springer 113-134. 

Zaitseva, E, Levashenko, V. 2013. Multiple-valued logic mathematical approaches for multi-state system reliability analysis. Journal of Applied Logic 11(3) 350-362. 

The classification is based on simple Boolean logic. Training data in n spectral bands are used in performing the classification. Brightness values from each pixel of the multi-spectral imagery are used to produce an -dimensional mean vector,... 

Logic level, however, is not a natural level for system designers. For example, when we want to indicate that 32-bit values of two variables, a and 6, sholild be added and stored in the third variable, c, we simply write the expression c = a + 6. We do not write 32 Boolean expressions with up to 64 variables each to indicate this simple operation. It is very difficult to imagine having complex multi-chip systems described in terms of 1 million or more Boolean equations. 

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