Can SD+ Make Proving Inconsistency Easier Than SD?

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SD and SD+ refer to Sentential Derivation systems used in propositional logic, where SD+ provides additional rules that serve as shortcuts for deriving conclusions. While SD focuses on the logical relations among molecular sentences derived from atomic sentences, SD+ aims to simplify the process of proving inconsistencies among sets of sentences. However, users often find SD+ challenging despite its intended ease, as the complexity of applying its rules effectively can lead to confusion. The discussion highlights that while SD+ is designed to streamline proofs, the intricacies of its application can make it more difficult for some to grasp compared to the standard SD approach.
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Why is SD+ so difficult?

I understand SD, but SD+ is eluding me..
 
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what's SD and SD+?
 
SD and SD+ stand for Sentential Derivation:
http://www.lawrence.edu/dept/philosophy/research/ryckmant/logic/sententi.htm


  • The sentential, or propositional, logic SL consists of a sentential language, SL, a semantic interpretation of that language, and a sentential derivation system, SD (and SD+).

    One might use SL to examine the logical relations among molecular or (compound) sentences generated from atomic (or simple) sentences.

    From SL's perspective, only molecular sentences have structure or form, and, therefore, SL is a logic that deals with relations obtaining among molecular sentences in virtue of their structure or form.
 
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If what you're seeking to prove can be proven using SD+, then it can be proven using SD. Since SD+ basically gives rules that work as shortcuts, shouldn't it be easier for me to prove that a set of sentences is inconsistent using SD+ and SD than it currently is?
 

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