Related papers: System Description: H-PILoT (Version 1.9)
Dedukti is a logical framework based on the lambda-Pi-calculus modulo rewriting, which extends the lambda-Pi-calculus with rewrite rules. In this paper, we show how to translate the proofs of a family of HOL proof assistants to Dedukti. The…
Research in robotic planning with temporal logic specifications, such as Linear Temporal Logic (LTL), has relied on single formulas. However, as task complexity increases, LTL formulas become lengthy, making them difficult to interpret and…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
Predicting and simulating aerodynamic fields for civil aircraft over wide flight envelopes represent a real challenge mainly due to significant numerical costs and complex flows. Surrogate models and reduced-order models help to estimate…
This paper proposes an adaptive human pilot model that is able to mimic the crossover model in the presence of uncertainties. The proposed structure is based on the model reference adaptive control, and the adaptive laws are obtained using…
We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently,…
We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from…
This paper introduces a new classification tool named Silas, which is built to provide a more transparent and dependable data analytics service. A focus of Silas is on providing a formal foundation of decision trees in order to support…
Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics,…
Subatomic systems were recently introduced to identify the structural principles underpinning the normalization of proofs. "Subatomic" means that we can reformulate logical systems in accordance with two principles. Their atomic formulas…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
Model Predictive Control (MPC) is widely used to operate safety-critical infrastructure by predicting future trajectories and optimizing control actions. However, nonlinear dynamics, hard safety constraints, and numerical optimization often…
This paper introduces Isabelle/HoTT, the first development of homotopy type theory in the Isabelle proof assistant. Building on earlier work by Paulson, I use Isabelle's existing logical framework infrastructure to implement essential…
Recent papers address the issue of updating the instance level of knowledge bases expressed in Description Logic following a model-based approach. One of the outcomes of these papers is that the result of updating a knowledge base K is…
This short paper describes a simple and intuitive Prolog program, a metainterpreter, that computes the bottom up meaning of a simple positive Horn clause definition. It involves a simple transformation of the object program rules into…
Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
We study the problem of $P$-interpolation, where $P$ is a set of binary predicate symbols, for certain classes of local extensions of a base theory. For computing the $P$-interpolating terms, we use a hierarchic approach: This allows us to…
In Inverse subsumption for complete explanatory induction Yamamoto et al. investigate which inductive logic programming systems can learn a correct hypothesis $H$ by using the inverse subsumption instead of inverse entailment. We prove that…