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A framework and methodology—termed LogiKEy—for the design and engineering of ethical
reasoners, normative theories and deontic logics is presented. The overall motivation is the …

Classical higher-order logic, when utilized as a meta-logic in which various other (classical
and non-classical) logics can be shallowly embedded, is suitable as a foundation for the …

We present a refutationally complete superposition calculus for a version of higher-order
logic based on the combinatory calculus. We also introduce a novel method of dealing with …

SMT solvers have throughout the years been able to cope with increasingly expressive
formulas, from ground logics to full first-order logic (FOL). In contrast, the extension of SMT …

We designed a superposition calculus for a clausal fragment of extensional polymorphic
higher-order logic that includes anonymous functions but excludes Booleans. The inference …

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics
and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based …

Superposition is among the most successful calculi for firstorder logic. Its extension to higher-
order logic introduces new challenges such as infinitely branching inference rules, new …

Decades of work have gone into develo** efficient proof calculi, data structures,
algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag …

We introduce refutationally complete superposition calculi for intentional and extensional
clausal λ-free higher-order logic, two formalisms that allow partial application and applied …