We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labelled with a representation of the arguments which support their validity. Arguments may then be… (More)
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept. This kind of uncertainty is called logical uncertainty. We define a concept of "acceptability" , which in duces a means… (More)
Classical logic has many appealing features for knowledge representation and reasoning. But unfortunately it is awed when reasoning about inconsistent information, since anything follows from a classical inconsistency. This problem is addressed by introducing the notions of \argument" and of \acceptability" of an argument. These notions are used to… (More)
Argumentation is the process of constructing arguments about propositions, and the assign ment of statements of confidence to those propo sitions based on the nature and relative strength of their supporting arguments. The process is modelled as a labelled deductive system, in which propositions are doubly labelled with the grounds on which they are based… (More)
The original deenition of reenement proof obligations in VDM is reviewed and examples are discussed which, while being intuitively sensible, pose problems for this deenition of reenement. An extended VDM reenement relation is introduced, to cope with the problems. Some non-standard applications of the extended reenement proof obligations are discussed.