<p>In order that epistemic formulas might be coupled with approximate databases, it is necessary to have a well-defined semantics for the knowledge operator and a method of reducing epistemic formulas to approximate formulas. In this thesis, two possible definitions of a semantics for the knowledge operator are proposed for use together with an approximate relational database: </p><p>* One based upon logical entailment (being the dominating notion of knowledge in literature); sound and complete rules for reduction to approximate formulas are explored and found not to be applicable to all formulas. </p><p>* One based upon algorithmic computability (in order to be practically feasible); the correspondence to the above operator on the one hand, and to the deductive capability of the agent on the other hand, is explored.</p><p>Also, an inductively defined semantics for a"know whether"-operator, is proposed and tested. Finally, an algorithm implementing the above is proposed, carried out using Java, and tested.</p>

In order that epistemic formulas might be coupled with approximate databases, it is necessary to have a well-defined semantics for the knowledge operator and a method of reducing epistemic formulas to approximate formulas. In this thesis, two possible definitions of a semantics for the knowledge operator are proposed for use together with an approximate relational database: * One based upon logical entailment (being the dominating notion of knowledge in literature); sound and complete rules for reduction to approximate formulas are explored and found not to be applicable to all formulas. * One based upon algorithmic computability (in order to be practically feasible); the correspondence to the above operator on the one hand, and to the deductive capability of the agent on the other hand, is explored. Also, an inductively defined semantics for a"know whether"-operator, is proposed and tested. Finally, an algorithm implementing the above is proposed, carried out using Java, and tested.