Inferences logical connectives

Obviously we should not allow multiple iterations of the same rule to increase the value of the consequent. If this were to be allowed then one could obtain any final value by simply re-iterating the same rule sufficient times. But redundancies in rules arise in subtle ways, e.g, B => A and C => A where B <-> C, i.e, B is another name for C. Finally, it can be shown that even if the chain of relation between B and C contains logical connectives other than <->, then allowing two successive inferences to increase the value of the consequence above that inferred by the strongest alone can lead to problems. 

Logical Connectives For reasoning and inferring on the basis of the internal knowledge presentation, the relationships or relations have to be described. This is feasible with logical connectives, as we know already from Section 1.1 (Table 1.2). Important connectives for compound propositions of p and q are as follows ... 

Deduction By means of logical connectives, correct inferences can be derived in the sense of deductive reasoning. In general, for deduction, true axioms (postulates) are given and the conclusions drawn are again true. This is denoted a legal inference. 

Any rule base should have IF-THEN implications in its structure and they provide the generation pattern of the phenomenon leading to inference engine search for the patterns embedded in the rules in such a manner that they match the overall qualitative and quantitative validities. In a rule base IF means when the condition is true, THEN means take action. In many cases, there is also another word as ELSE after IF-THEN, which means that when the condition (rule) is not true take another action (rule). In the logical connectives ELSE corresponds to OR , and hence to ORing action. Some of the examples are as follows. 

After deciding about the inputs and outputs of phenomenon logical statements (rule bases) can be written down by convenient cooperation of logical connectives, especially in the antecedent part. In order to achieve successM rule bases, one should appreciate, understand and know the conunon language implications of each connective. In daily conununications these connectives are used automatically and unconsciously in a frequent manner, without instantaneous distinction between their implications within a sentence, whether it is logical or not. However, for rational, scientific and objective inferences, one should know distinctions and implications of each logical connective. 

Reverse engineering has been demonstrated to work in principle for model genetic networks of binary genes connected through logical rules [18]. A key issue is the data requirement necessary to provide sufficient information to capture the complexity of the molecular network. In model networks it has been shown that only a tiny subset of all possible behaviors need to be known in order to infer network architecture with accuracy [18], provided that the network exhibits significant constraints (biomolecular networks are far removed from randomly connected networks) [20]. 

The topic of this chapter may seem like a digression from methods and approaches to reaction mechanisms, but it is not it is an introduction to it. We worked on both topics for some time and there is a basic connection. Think of an electronic device and ask how are the logic functions of this device determined Electronic inputs (voltages and currents) are applied and outputs are measured. A truth table is constructed and from this table the logic functions of the device, and at times some of its components, may be inferred. The device is not subjected to the approach toward a chemical mechanism described in the previous chapter, of taking the device apart and testing its simplest components. (That may have to be done sometimes but is to be avoided if possible.)... 

We say that the grounds support the claim on the basis of the existence of a warrant that explains the connection between the grounds and the claim. It is easy to relate the structure of these basic elements with the process of inference, whether inductive or deductive, in classical logic. The warrants are the set of rules of inference, and the grounds and claim are the set of well-defined propositions or statements. It will be only the sequence and procedures, as used to formulate the three basic elements and their structure in a logical fashion, that will determine the type of inference that is used. 

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. 

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