Modelling enthymemes Sample Clauses

Modelling enthymemes. ‌ In this Section we define enthymemes, their properties and their different types of exten- sions. In this thesis we define an enthymeme E as a forest of labelled trees whose nodes are labelled either with an element α ∈ L or an inference rule r, and if two nodes n1 and n2 are connected (where n1 is the parent of n2), then either the label l1 of n1 is a literal, the label l2 of n2 is an inference rule and l1 is the conclusion of l2, or l1 is an inference rule, l2 is a literal and l2 is an antecedent of l1 (e.g., see the enthymeme E in Figure 3.3.(ii)). Definition 19 (Enthymeme). Let AS = ⟨L, ( · ), R, nom⟩, where R = Rs ∪ Rdef, and AT = ⟨AS, K⟩. An enthymeme E is a forest of labelled trees E = ⟨Nd(E), Ed(E), labE⟩ such that Nd(E) ̸= 0/ and conditions 1 and 2 from Definition 18 hold. Additionally, we define the following characteristics of an enthymeme: – Roots(E) = {n | n ̸∈ Children(E)}; – Leaves(E) = {n | n ̸∈ Parents(E)}; – Prem(E) = {n | n ∈ Leaves(E) and labE (n) ∈ L}; – Rules(E) = {n | n ∈ Nd(E) and labE (n) ∈ R}; – StrictRules(E) = {r | r ∈ Rules(E) and labE (r) ∈ Rs}; – DefRules(E) = {r | r ∈ Rules(E) and labE (r) ∈ Rdef}. We, also, define an enthymeme E′ of an enthymeme E as an enthymeme whose nodes and edges are a subset of the nodes and edges of E, and the label of each node in E′ is the same label of the corresponding node in E (e.g., see the enthymeme E′ of the enthymeme E in Figure 3.3.(ii)). Note that our definition of an enthymeme (see Definition 19) allows different enthymematic routes between explicit components. However, if one wants to reconstruct an enthymeme E specifically back to the intended argument A from which E was generated, then different enthymematic routes will lead to different arguments. For example, looking at Figure 3.3.(i), if we connect the node n5 (labelled c) to the node n15 (labelled s, t ⇒ c) and the node n13 (labelled c) to the node n8 (labelled a, b ⇒ c) then formally the argument we obtain is different to the argument A depicted in Figure 3.3.(i). As explained earlier, we do this to differentiate between distinct instances of the same literal in the same argument and be able to refer to the specific characteristics of these instances, something we will need in Section 5.2.2 where we discuss honest agents. Definition 20 (Enthymeme of an enthymeme). Let E be an enthymeme. An enthymeme E′ of E (written E′ ≤ E) is a forest of labelled trees E′ = ⟨Nd(E′), Ed(E′), labE′⟩ such that: