Abstract
Syntactic or symbolic approaches to logic began from the middle of nineteenth century. G. Boole attempted to express logical inference as an algebraic calculation in his book Boole 1854. It took several decades before Hilbert-style formal systems were introduced.
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Notes
- 1.
Davey and Priestley 2002 will be a useful guide to topics in this chapter. Anyone familiar with the book can skip the present chapter except Sect. 6.5.
- 2.
We use sometimes the word ‘iff’ as an abbreviation of ‘if and only if’ in the following, as we have already stated in Part I.
- 3.
Sometimes, assignments are called valuations. But in our book we use the word ‘valuations’ only in the context of Kripke semantics (see Chap. 10).
- 4.
In Part II, the word ‘validity’ is used in this general sense.
- 5.
These chains were discussed in Gödel (1932).
- 6.
The logic is named after K. Gödel and also M. Dummett (1959).
- 7.
His result was reported in Łukasiewicz and Tarski (1930).
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Ono, H. (2019). From Algebra to Logic. In: Proof Theory and Algebra in Logic. Short Textbooks in Logic. Springer, Singapore. https://doi.org/10.1007/978-981-13-7997-0_6
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DOI: https://doi.org/10.1007/978-981-13-7997-0_6
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