Related papers: Faithful Logic Embeddings in HOL -- Deep and Shall…
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…
A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. This embedding is proven sound and complete, that is, faithful. The work presented here provides the theoretical…
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…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…
We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…
A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic.…
We present an approach towards the deep, pluralistic logical analysis of argumentative discourse that benefits from the application of state-of-the-art automated reasoning technology for classical higher-order logic. Thanks to its…
Many foundational program verification tools have been developed to build machine-checked program correctness proofs, a majority of which are based on Hoare logic. Their program logics, their assertion languages, and their underlying…
This position statement looks back on two decades of work on shallow embeddings of non-classical logics in classical higher-order logic (HOL), a line of research that expanded into a range of logic embeddings in HOL and inspired the LogiKEy…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
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…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
The paper presents a comprehensive analysis of the European AI Act in terms of its logical modalities, with the aim of preparing its formal representation, for example, within the logic-pluralistic Knowledge Engineering Framework and…
We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…