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In order to analyze the behavior of a system at successive moments in time, while staying within the limitations of propositional logic, it is necessary to create independent alphabets of logical features for each moment of time that we contemplate using in our discussion. These moments have reference to typical instances and relative intervals, not actual or absolute times. For example, to discuss ''velocities'' (first order rates of change) we need
In order to analyze the behavior of a system at successive moments in time, while staying within the limitations of propositional logic, it is necessary to create independent alphabets of logical features for each moment of time that we contemplate using in our discussion. These moments have reference to typical instances and relative intervals, not actual or absolute times. For example, to discuss ''velocities'' (first order rates of change) we need to consider points of time in pairs. There are a number of natural ways of doing this. Given an initial alphabet, we could use its symbols as a lexical basis to generate successive alphabets of compound symbols, say, with temporal markers appended as suffixes.
to consider points of time in pairs. There are a number of natural ways of doing this. Given an initial alphabet, we could use its symbols as a lexical basis to generate successive alphabets of compound symbols, say, with temporal markers appended as suffixes.
As a standard way of dealing with these situations, I produce the following scheme of notation, which extends any alphabet of logical features through as many temporal moments as a particular order of analysis may demand. The lexical operators p<sup>''k''</sup> and Q<sup>''k''</sup> are convenient in many contexts where the accumulation of prime symbols and union symbols would otherwise be cumbersome.
As a standard way of dealing with these situations, the following scheme of notation suggests a way of extending any alphabet of logical features through as many temporal moments as a particular order of analysis may demand. The lexical operators <math>\operatorname{p}^k</math> and <math>\operatorname{Q}^k</math> are convenient in many contexts where the accumulation of prime symbols and union symbols would otherwise be cumbersome.
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