Related papers: Reasoning About Higher-Order Relational Specificat…
The dependently-typed lambda calculus LF is often used as a vehicle for formalizing rule-based descriptions of object systems. Proving properties of object systems encoded in this fashion requires reasoning about formulas over LF typing…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the…
What-if (provisioning for an update to a database) and how-to (how to modify the database to achieve a goal) analyses provide insights to users who wish to examine hypothetical scenarios without making actual changes to a database and…
Many important functional and security properties--including non-interference, determinism, and generalized non-interference (GNI)--are hyperproperties, i.e., properties relating multiple executions of a program. Existing separation logics…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
Sandqvist's base-extension semantics for intuitionistic propositional logic defines a support relation parametrised by atomic bases, with validity identified as support in every base. Sandqvist's completeness theorem answers the global…
Felty and Miller have described what they claim to be a faithful encoding of the dependently typed lambda calculus LF in the logic of hereditary Harrop formulas, a sublogic of an intuitionistic variant of Church's Simple Theory of Types.…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and quantitative…
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…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
Domain-specific heuristics are an essential technique for solving combinatorial problems efficiently. Current approaches to integrate domain-specific heuristics with Answer Set Programming (ASP) are unsatisfactory when dealing with…
Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar (HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a language is defined entirely in terms of provability in the single logical system.…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
In view of the paradigm shift that makes science ever more data-driven, in this paper we consider deterministic scientific hypotheses as uncertain data. In the form of mathematical equations, hypotheses symmetrically relate aspects of the…