Kenclauses

Kenclauses are a class of logical clauses used in knowledge representation and automated reasoning. They are disjunctions of literals over a finite set of propositional variables, similar in form to clauses in conjunctive normal form (CNF), but defined with a specific constraint that distinguishes them from ordinary CNF clauses.

The defining feature of kenclauses is a bound on negation within a clause. For a fixed nonnegative integer k, a kenclause is a disjunction L = l1 ∨ l2 ∨ ... ∨ ln where each li is a literal on variables from V, and the number of negative literals in L is at most k. This constraint yields a spectrum of fragments: k = 0 yields monotone clauses (no negations), while larger k allows more expressive power but preserves the ken-clause structure.

Semantics and use: Kenclauses are intended to support efficient satisfiability checking for certain parameter choices of k, enabling tractable reasoning in restricted knowledge bases. They can be compiled into standard CNF for use with conventional SAT solvers, or reasoned about directly within ken-specific inference rules.

Example: With k = 1 over variables {A, B, C}, a kenclause could be A ∨ B ∨ ¬C, which contains one negative literal.

Relationship to other formalisms: Kenclauses generalize monotone clauses and relate to restricted fragments such as Horn and dual-Horn under particular parameter settings. They serve as an intermediate abstraction between purely monotone clauses and general CNF in knowledge-centric applications.

See also: Horn clauses, monotone clauses, CNF, SAT.