Related papers: Separation Logic with Linearly Compositional Induc…

We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…

Following the recent push for trustworthy AI, there has been an increasing interest in developing contrastive explanation techniques for optimisation, especially concerning the solution of specific decision-making processes formalised as…

Safety-critical controllers of complex systems are hard to construct manually. Automated approaches such as controller synthesis or learning provide a tempting alternative but usually lack explainability. To this end, learning decision…

The control properties of discrete-time switched linear systems (SLS) with switching signals generated by logical dynamic systems are studied using the semi-tensor product (STP) approach. With the algebraic state space representation…

We consider the broad problem of analyzing safety properties of asynchronous concurrent programs under arbitrary thread interleavings. Delay-bounded deterministic scheduling, introduced in prior work, is an efficient bug-finding technique…

Sequence generation and prediction form a cornerstone of modern machine learning, with applications spanning natural language processing, program synthesis, and time-series forecasting. These tasks are typically modeled in an autoregressive…

We define a class of Separation Logic formulae, whose entailment problem: given formulae $\phi, \psi_1, \ldots, \psi_n$, is every model of $\phi$ a model of some $\psi_i$? is 2EXPTIME-complete. The formulae in this class are existentially…

This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…

Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…

This paper explores the theoretical limits of using discrete abstractions for nonlinear control synthesis. More specifically, we consider the problem of deciding continuous-time control with temporal logic specifications. We prove that…

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…

Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique…

This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…

Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture…

The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…

Learned Differentiable Boolean Logic Networks (DBNs) already deliver efficient inference on resource-constrained hardware. We extend them with a trainable, differentiable interconnect whose parameter count remains constant as input width…

For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs…

We introduce a novel variant of BSS machines called Separate Branching BSS machines (S-BSS in short) and develop a Fagin-type logical characterisation for languages decidable in non-deterministic polynomial time by S-BSS machines. We show…

We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…