Related papers: Goal-Oriented Conjecturing for Isabelle/HOL

A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning…

When doing inference in ProbLog, a probabilistic extension of Prolog, we extend SLD resolution with some additional bookkeeping. This additional information is used to compute the probabilistic results for a probabilistic query. In Prolog's…

Model execution allows us to prototype and analyse software engineering models by stepping through their possible behaviours, using techniques like animation and simulation. On the other hand, deductive verification allows us to construct…

In Isabelle/HOL, declarative proofs written in the Isar language are widely appreciated for their readability and robustness. However, some users may prefer writing procedural "apply-style" proof scripts since they enable rapid exploration…

We prove potential automorphy results for a single Galois representation $G_F \rightarrow GL_n(\overline{\mathbb{Q}}_l)$ where $F$ is a CM number field. The strategy is to use the $p,q$ switch trick and modify the Dwork motives employed in…

In this paper we present an efficient approach to implementing model checking in the Higher Order Logic (HOL) of Isabelle. This is a non-trivial task since model checking is restricted to finite state sets. By restricting our scope to…

This paper presents a novel approach to premise selection, a crucial reasoning task in automated theorem proving. Traditionally, symbolic methods that rely on extensive domain knowledge and engineering effort are applied to this task. In…

Formal verification of cyber-physical and robotic systems requires that we can accurately model physical quantities that exist in the real-world. The use of explicit units in such quantities can allow a higher degree of rigour, since we can…

Many facts possess symmetrical counterparts that often require a separate formal proof, depending on the nature of the involved symmetry. We introduce a method in Isabelle/HOL which produces such a symmetrical fact for the list datatype and…

Expected goals (xG) models estimate the probability that a shot results in a goal from its context (e.g., location, pressure), but they operate only on observed shots. We propose xG+, a possession-level framework that first estimates the…

We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…

For recursive functions general principles of induction needs to be applied. Instead of verifying them directly using the Vienna Development Method Specification Language (VDM-SL), we suggest a translation to Isabelle/HOL. In this paper,…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

Designing better machine translation systems by considering auxiliary inputs such as images has attracted much attention in recent years. While existing methods show promising performance over the conventional text-only translation systems,…

Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…

We address goal-based imitation learning, where the aim is to output the symbolic goal from a third-person video demonstration. This enables the robot to plan for execution and reproduce the same goal in a completely different environment.…

We introduce a linguistically enhanced combination of pre-training methods for transformers. The pre-training objectives include POS-tagging, synset prediction based on semantic knowledge graphs, and parent prediction based on dependency…

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…

The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…

We study temporally extended goals expressed in Pure-Past LTL (PPLTL). PPLTL is particularly interesting for expressing goals since it allows to express sophisticated tasks as in the Formal Methods literature, while the worst-case…