A Parameterised Hierarchy of Argumentation Semantics for Extended Logic Programming and its Application to the Well-founded Semantics

Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships between the semantics and examine some essential properties concerning consistency and the coherence principle, which relates default negation and explicit negation. Most significantly, we place existing semantics put forward in the literature in our hierarchy and identify a particular argumentation semantics for which we prove equivalence to the paraconsistent well-founded semantics with explicit negation, WFSX$_p$. Finally, we present a general proof theory, based on dialogue trees, and show that it is sound and complete with respect to the argumentation semantics.Comment: To appear in Theory and Practice of Logic Programmin

A Categorical and Graphical Treatment of Closure Conversion

This paper gives a formal basis for the closure conversion phase of functional programming languages with imperative features, using a graphical semantics for the language. We present normal forms of graphs, one corresponding to procedural languages, and one corresponding to object-oriented languages. Using closure conversion, we can prove normalization results for both normal forms. Thus, we obtain sound algorithms for compiling the language into either procedural or object-oriented code. We discuss efficiency issues of the translation and suggest some improvements on the algorithm. 1 Introduction This paper describes a categorical formalization of an important step in compiling higher-order languages: closure conversion. Closure conversion is a compilation step which takes nested procedures such as: proc f (x : X1) : X2 { rec g; proc g (y : Y1) : Y2 { return G (g, x, y); } return F (g, x); } and lifts the nested procedures up to top level: rec g_lift; proc g_lift (x : X1, y : Y1..