Modelling socio-political competition

Abstract

This paper continues the investigation of the logic of competing theories (be they scientific, social, political etc.) initiated in [4]. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired by Ploica's representation of general lattices. We axiomatize the resulting many-valued, non-distributive modal logic of these structures and prove a completeness theorem. We illustrate the application of this logic through a case study in which we model competition among interacting political promises and social demands within an arena of political parties social groups.

Modelling competing theories

“…Recall that for all f : A × Z → A, and u : Z → A, the maps 2 f ↑ : Z → A and u ↓ : A × Z → A are respectively defined by the assignments (R [1] [{β/z}]) [10] ⊆ R [1] [{β/z}]…”

“…So we propose, for β = 0, to assign a truth-value of 0.8 to ψ at z A and z H , and a truth-value of 0.4 to ψ at z M , a strong discount due to the guesswork needed to accommodate the testing of ψ on z M . 10 The following We are now in a position to compute the extensions of M ϕ, H ϕ, M ψ and H ψ. 11 Intuitively, X χ can be understood as what becomes of hypothesis χ when 'seen through the lenses' of theory X.…”

“…Let us show that (R [1] [{β/(α, z)}]) [10] ⊆ R [1] [{β/(α, z)}]. By definition, for every w ∈ Z A , [1] [{β/(α, z)}]) [10] [1] [{β/(α, z)}]) [1]…”

Modelling Informational Entropy

“…The following lemma is an immediate consequence of Lemma 9 in the appendix, using Lemma 3 and the observation in Footnote 6. [y]) [10] ⊆ R [0] [y] for every y ∈ Z;…”

“…6 Applying the notation (2) to a graph-based L-frame F, we will sometimes abbreviate E [0] [Y] and E [1] [B] as Y [0] and B [1] , respectively, for each Y, B ⊆ Z. If Y = {y} and B = {b}, we write y [0] and b [1] for {y} [0] and {b} [1] , and write Y [01] and B [10] for (Y [0] ) [1] and (B [1] ) [0] , respectively. Notice that, by Lemma 3,…”