Relational Representation Theorems for Some Lattice-Based Structures
نویسندگان
چکیده
The major elements of the method of proving relational representation theorems presented in this paper are, on the one hand, Urquhart representation theorem for lattices [17] and Allwein and Dunn developments on Kripke semantics for linear logic (see [1] and also [4]), and on the other hand, a generalisation of Jonsson and Tarski ideas [9] which inspired the developments in [5], [6] and [13]. We present an extension of the Urquhart-Allwein-Dunn (UAD) methodology to lattice-based modal algebras, lattice-based relation algebras and algebras of substructural logics. Our generalisation of the UAD framework requires the following steps:
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