Abstract
In this chapter, we give a short introduction to residuated structures which are algebraic structures for substructural logics. Boolean algebras and also Heyting algebras are defined to be lattice structures with a binary relation \(\rightarrow \) which satisfy the law of residuation between \(\wedge \) and \(\rightarrow \), i.e., \(a \wedge b \le c\) iff \(a \le b \rightarrow c\), for all a, b, c.
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Notes
- 1.
It is recommended to have a brief look at Sect. 5.5 before starting to read the present chapter.
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Ono, H. (2019). Residuated Structures. In: Proof Theory and Algebra in Logic. Short Textbooks in Logic. Springer, Singapore. https://doi.org/10.1007/978-981-13-7997-0_9
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DOI: https://doi.org/10.1007/978-981-13-7997-0_9
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