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Knowledge bases and expert systems are usually production rules systems and as such they lack expressive means for expressing modalities like "agent believes in statement", "agent has duty to perform action", "agent has permission to perform action". Modalities are usualy written as modal operators (diamond and square boxes) or as special kind of implications. https://ts.data61.csiro.au/publications/nictaabstracts/5627.pdf is good example how to introduce modalities in defeasible logic without Kripke/relational/possible world semantics/machinery.

Introduction of modalities introduces both new symbols in language and new inference rules in language (like permission follows from duty), https://en.wikipedia.org/wiki/Modal_logic contains list of good examples of rules that are brought with introduction of modal operators.

So - my question is - how to introduce modalities in expert systems / production rule systems which have no dedicated operators or implications for modalities?

My proposal is to treat modalities as predicates and introduce special kind of metarules that for each type of modal predicate generate relevant modal predicates. E.g. which for duty-predicate generates permissions-predicate. There is book about such approach http://www.springer.com/us/book/9783319225562

Is my proposal about modalities as special kind of predicates sound, are there alternatives?

Specifically, I am trying to introduce modalities http://opencog.org/, this system support meta-rules and higher-order rules, so my approach maybe is valid and academically acceptable?

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  • $\begingroup$ Important point: the result of predicate evaluation is truth value, but the result of (modal) operator application is other sentence. So, some reformulation is needed, but it may work. $\endgroup$ – TomR Mar 14 '17 at 21:31

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