Related papers: Extracting Higher-Order Goals from the Mizar Mathe…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…
A strictly formal, set-theoretical treatment of classical first-order logic is given. Since this is done with the goal of a concrete Mizar formalization of basic results (Lindenbaum lemma; Henkin, satisfiability, completeness and…
We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
Higher-order constructs enable more expressive and concise code by allowing procedures to be parameterized by other procedures. Assertions allow expressing partial program specifications, which can be verified either at compile time…
In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
Linearisability is a central notion for verifying concurrent libraries: a given library is proven safe if its operational history can be rearranged into a new sequential one which, in addition, satisfies a given specification.…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and…
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…
In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…