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 Declarative Foundation of λProlog with Equality

We build general model-theoretic semantics for higher-order logic programming languages. Usual semantics for first-order logic is two-level: i.e., at a lower level we define a domain of individuals, and then, we define satisfaction of formulas with respect to this domain. In a higher-order logic which includes the propositional type in its primitive set of types, the definition of satisfaction of formulas is mutually recursive with the process of evaluation of terms. As result of this in higher-order logic it is extremely difficult to define an effective semantics. For example to define T p operator for logic program P, we need a fixed domain without regard to interpretations. In usual semantics for higher-order logic, domain is dependent on interpretations. We overcome this problem and argue that our semantics provides a more suitable declarative basis for higher-order logic programming than the usual general model semantics. We develop a fix point semantics based on our model. We also show that a quotient of the domain of our model can be the domain of a model for higher-order logic programs with equality

Logic-Based Decision Support for Strategic Environmental Assessment

Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logic-based approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages.Comment: 17 pages, 1 figure, 26th Int'l. Conference on Logic Programming (ICLP'10