The simple substitution property of the intermediate propositional logics on finite slices
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The simple substitution property provides a systematic and easy method for proving a theorem by an axiomatic way. The notion of the property was introduced in Hosoi  but without a definite name and he showed three examples of the axioms with the property. Later, the property was given it's name as above in Sasaki .
Our main result here is that the necessary and sufficient condition for a logicL on a finite slice to have the simple substitution property is thatL is finite. Here the necessity part is essentially new, for the sufficiency part has been proved in Hosoi and Sasaki . Also the proof of sufficiency part is improved here.
For logics on the ω-th slice, the condition for them to have the simple substitution property is not yet known.
We abbreviate the simple substitution property asSSP.
KeywordsMathematical Logic Computational Linguistic Propositional Logic Easy Method Simple Substitution
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