Can SD+ Make Proving Inconsistency Easier Than SD?

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Discussion Overview

The discussion centers around the complexities of proving inconsistency using two systems of sentential derivation: SD and SD+. Participants explore the differences between these systems and the implications for logical proofs.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses difficulty in understanding SD+, despite having a grasp of SD.
  • Another participant seeks clarification on the definitions of SD and SD+.
  • A third participant provides a brief overview of SD and SD+, explaining their roles in sentential logic and how they relate to molecular sentences.
  • One participant posits that if a proof can be achieved using SD+, it should also be achievable using SD, suggesting that SD+ offers shortcuts that could simplify proving inconsistency.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus on whether SD+ truly simplifies the process of proving inconsistency compared to SD, with differing views on the effectiveness of the two systems.

Contextual Notes

Participants have not fully explored the assumptions underlying the effectiveness of SD+ as a shortcut, nor have they resolved the complexities involved in proving inconsistency.

Who May Find This Useful

Readers interested in sentential logic, logical proofs, and the comparative analysis of derivation systems may find this discussion relevant.

Marie120
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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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