Defeasible Reasoning and Degrees of Justification

1.1 Argument-based Defeasible Reasoning. We can think of a defeasible reasoner in either of two ways. First, it might be a tool for use by a human operator who supplies it with premises comprising its background knowledge and premises representing newly acquired information. Alternatively, a defeasible reasoner might be a model of the reasoning of a human being or other generally intelligent agent (GIA — see Pollock 2008, 2008a, 2008b). The main difference is that a GIA must acquire its own premises as part of its own cognition. Such premises can be viewed as the output of the agent’s sensors, which are input to the agent’s reasoning. I will assume an argument-based approach to defeasible reasoning, of the sort I have employed regularly in the past (Pollock 1995, 2009). The current state of a defeasible reasoner can be represented by an inference-graph. This is a directed graph, where the nodes represent the conclusions of arguments (or premises, which can be regarded as a special kind of conclusion). There are two kinds of links between the nodes. Supportlinks represent inferences, diagramming how a conclusion is supported via a single inferencescheme applied to conclusions contained in the inference-graph. Defeat-links diagram defeat relations between defeaters and what they defeat. For more details, so Pollock (2009). Inferences proceed via inference-schemes, which license inferences. We can take an inference scheme to be a datastructure one slot of which consists of a set of premises (written as open formulas), a second slot of which consists of the conclusion (written as an open formula), and a third slot lists the scheme variables, which are the variables occurring in the premises and conclusion. Inference schemes license new inferences, which is to say that they license the addition of nodes and inference-links to a pre-existing inference-graph. Equivalently, they correspond to clauses in the recursive definition of “inference-graph”. The inference-graph representing the current state of the cognizer’s reasoning “grows” by repeated applyication of inference-schemes to conclusions already present in the inference-graph and adding the conclusion of the new inference to the inference-graph. When a conclusion is added to an inference-graph, this may also result in the addition of new defeat-links to the inference-graph. A new link may either record the fact that the new conclusion is a defeater or some previously recorded inference in the inference-graph, or the fact that some previously recorded conclusion is a defeater for the new inference.