Many-valued Logic Programming Research Articles

Rumpole

Access control policies define what resources can be accessed by which subjects and under which conditions. It is, however, often not possible to anticipate all subjects that should be permitted access and the conditions under which they should be permitted. For example, predicting and correctly encoding all emergency and exceptional situations is impractical. Traditional access control models simply deny all requests that are not permitted, and in doing so may cause unpredictable and unacceptable consequences. To overcome this issue, break-glass access control models permit a subject to override an access control denial if he accepts a set of obligatory actions and certain override conditions are met. Existing break-glass models are limited in how the override decision is specified. They either grant overrides for a predefined set of exceptional situations, or they grant unlimited overrides to selected subjects, and as such, they suffer from the difficulty of correctly encoding and predicting all override situations and permissions. To address this, we develop Rumpole, a novel break-glass language that explicitly represents and infers knowledge gaps and knowledge conflicts about the subject's attributes and the contextual conditions, such as emergencies. For example, a Rumpole policy can distinguish whether or not it is known that an emergency holds. This leads to a more informed decision for an override request, whereas current break-glass languages simply assume that there is no emergency if the evidence for it is missing. To formally define Rumpole, we construct a novel many-valued logic programming language called Beagle. It has a simple syntax similar to that of Datalog, and its semantics is an extension of Fitting's bilattice-based semantics for logic programs. Beagle is a knowledge non-monotonic langauge, and as such, is strictly more expressive than current many-valued logic programming languages.

Powersets of terms and composite monads

Composing various powerset functors with the term monad gives rise to the concept of generalized terms. This in turn provides a technique for handling many-valued sets of terms in a framework of variable substitutions, thus being the prerequisite for categorical unification in many-valued logic programming using an extended notion of terms. As constructions of monads involve complicated calculations with natural transformations, proofs are supported by a graphical approach that provides a useful tool for handling various conditions, such as those well known for distributive laws.

Similarities between powersets of terms

Generalisation of the foundational basis for many-valued logic programming builds upon generalised terms in the form of powersets of terms. A categorical approach involving set and term functors as monads allows for a study of monad compositions that provide variable substitutions and compositions thereof. In this paper, substitutions and unifiers appear as constructs in Kleisli categories related to particular composed powerset term monads. Specifically, we show that a frequently used similarity-based approach to fuzzy unification is compatible with the categorical approach, and can be adequately extended in this setting; also some examples are included in order to illuminate the definitions.

Many-valued logic and mixed integer programming

We generalize prepositional semantic tableaux for classical and many-valued logics toconstraint tableaux. We show that this technique is a generalization of the standard translation from CNF formulas into integer programming. The main advantages are (i) a relatively efficient satisfiability checking procedure for classical, finitely-valued and, for the first time, for a wide range of infinitely-valued propositional logics; (ii) easy NP-containment proofs for many-valued logics. The standard translation of two-valued CNF formulas into integer programs and Tseitin's structure preserving clause form translation are obtained as a special case of our approach.