Logic, Reasoning and A Programming Language for Simulating Economic and Business Processes with Artificially Intelligent Agents

7 Formal Logic and SDML

As SDML is a declarative language it is already close to being a logic. Rules are stated as logical relationships between facts such that if the antecedents are true so are the consequents. These rules are specified beforehand by the modeller to determine the general actions of each agent in the model*1. Once the model rules and starting facts are established by the modeller, the inference machinery of SDML animates the model by determining the logical consequences of the facts and the rules at each time period in succession. Continuity is established by the fact that many of these rules will refer to facts established in previous time periods.

The logic of SDML's propositional inference machinery is equivalent to a fragment of Konlige's strongly grounded autoepsitemic logic (SG-AE) [5]. This is the logic of reasoning with introspection - the ability to reason about one's own beliefs. Belief for a human reasoner corresponds to inference in SDML. This mainly effects the treatment of negation, which in SDML is implemented with the notInferred primitive.

In most normal circumstances this acts as normal negation, since all positive logical implications of the model are inferred, if something is not true (from the point of view of the model) then it will be not inferred. In some circumstances, you are allowed to start with an assumption that something is not inferred until shown otherwise (usually by another rule firing). If rules conflict with each other, SDML can re-trace its inference and try another possible SG-AE extension of the original model. If no such extensions are possible then an error message arises and the simulation halts.

Thus, in the absence of logical errors by the modeller, SDML produces a possible animation of the modeller's original rules and facts given some reasonable assumptions about the model.

Logic, Reasoning and A Programming Language for Simulating Economic and Business Processes with Artificially Intelligent Agents - 12 APR 96

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