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Extracting relevant features from data sets where the number of observations ($n$) is much smaller then the number of predictors ($p$) is a major challenge in modern statistics. Sorted L-One Penalized Estimation (SLOPE), a generalization of…

Verification conditions (VCs) are logical formulas whose satisfiability guarantees program correctness. We consider VCs in the form of constrained Horn clauses (CHC) which are automatically generated from the encoding of (an interpreter of)…

We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…

We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense),…

We prove that capability safety admits an exact representation as propositional Datalog evaluation (Datalogprop: the monadic, ground, function-free fragment of first-order logic), enabling the transfer of algorithmic and structural results…

A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid…

Strategy logic (SL) is a powerful temporal logic that enables strategic reasoning in multi-agent systems. SL supports explicit (first-order) quantification over strategies and provides a logical framework to express many important…

We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…

The randomised Horn problem, in both its additive and multiplicative version, has recently drawn increasing interest. Especially, closed analytical results have been found for the rank-1 perturbation of sums of Hermitian matrices and…

SystemVerilog Assertions (SVAs) are essential for verifying Register Transfer Level (RTL) designs, as they can be embedded into key functional paths to detect unintended behaviours. During simulation, assertion failures occur when the…

A well-established approach to proving progress properties such as deadlock-freedom and termination is to associate obligations with threads. For example, in most existing work the proof rule for lock acquisition prescribes a standard usage…

Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…

The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems,…

We propose a technique for declaratively specifying strategies for semi-supervised learning (SSL). The proposed method can be used to specify ensembles of semi-supervised learning, as well as agreement constraints and entropic…

We present a new soundness proof of Concurrent Separation Logic (CSL) based on a structural operational semantics (SOS). We build on two previous proofs and develop new auxiliary notions to achieve the goal. One uses a denotational…

This paper describes a deductive approach to synthesizing imperative programs with pointers from declarative specifications expressed in Separation Logic. Our synthesis algorithm takes as input a pair of assertions---a pre- and a…

Assertion checking is an invaluable programmer's tool for finding many classes of errors or verifying their absence in dynamic languages such as Prolog. For Prolog programmers this means being able to have relevant properties such as modes,…

Large language models (LLMs) have achieved impressive results on multi-step mathematical reasoning, yet at the cost of high computational overhead. This challenge is particularly acute for test-time scaling methods such as parallel…