Learning representations that capture rich semantic relationships and accommodate propositional calculus poses a significant challenge. Existing approaches are either contrastive, lacking theoretical guarantees, or fall short in effectively representing the partial orders inherent to rich visual-semantic hierarchies. In this paper, we propose a novel approach for learning visual representations that not only conform to a specified semantic structure but also facilitate probabilistic propositional reasoning. Our approach is based on a new nuclear norm-based loss. We show that its minimum encodes the spectral geometry of the semantics in a subspace lattice, where logical propositions can be represented by projection operators.

Statistical methods have been widely misused and misinterpreted in various scientific fields, raising significant concerns about the integrity of scientific research. To develop techniques to mitigate this problem, we propose a new method for formally specifying and automatically verifying the correctness of statistical programs. In this method, programmers are reminded to check the requirements for statistical methods by annotating their source code. Then, a software tool called StatWhy automatically checks whether the programmers have properly specified the requirements for the statistical methods. This tool is implemented using the Why3 platform to verify the correctness of OCaml programs for statistical hypothesis testing. We demonstrate how StatWhy can be used to avoid common errors in a variety of popular hypothesis testing programs.

Causal discovery amounts to unearthing causal relationships amongst features in data. It is a crucial companion to causal inference, necessary to build scientific knowledge without resorting to expensive or impossible randomised control trials. In this paper, we explore how reasoning with symbolic representations can support causal discovery. Specifically, we deploy assumption-based argumentation (ABA), a well-established and powerful knowledge representation formalism, in combination with causality theories, to learn graphs which reflect causal dependencies in the data. We prove that our method exhibits desirable properties, notably that, under natural conditions, it can retrieve ground-truth causal graphs. We also conduct experiments with an implementation of our method in answer set programming (ASP) on four datasets from standard benchmarks in causal discovery, showing that our method compares well against established baselines.

We introduce a data-driven approach to computing finite bisimulations for state transition systems with very large, possibly infinite state space. Our novel technique computes stutter-insensitive bisimulations of deterministic systems, which we characterize as the problem of learning a state classifier together with a ranking function for each class. Our procedure learns a candidate state classifier and candidate ranking functions from a finite dataset of sample states; then, it checks whether these generalise to the entire state space using satisfiability modulo theory solving. Upon the affirmative answer, the procedure concludes that the classifier constitutes a valid stutter-insensitive bisimulation of the system. Upon a negative answer, the solver produces a counterexample state for which the classifier violates the claim, adds it to the dataset, and repeats learning and checking in a counterexample-guided inductive synthesis loop until a valid bisimulation is found. We demonstrate on a range of benchmarks from reactive verification and software model checking that our method yields faster verification results than alternative state-of-the-art tools in practice. Our method produces succinct abstractions that enable an effective verification of linear temporal logic without next operator, and are interpretable for system diagnostics.

Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. In this paper, we study an instantiation-based approach for reasoning in possibly non-flat ABA. We make use of a semantics-preserving translation between ABA and bipolar argumentation frameworks (BAFs). By utilizing compilability theory, we establish that the constructed BAFs will in general be of exponential size. In order to keep the number of arguments and computational cost low, we present three ways of identifying redundant arguments. Moreover, we identify fragments of ABA which admit a poly-sized instantiation. We propose two algorithmic approaches for reasoning in possibly non-flat ABA. The first approach utilizes the BAF instantiation while the second works directly without constructing arguments. An empirical evaluation shows that the former outperforms the latter on many instances, reflecting the lower complexity of BAF reasoning. This result is in contrast to flat ABA, where direct approaches dominate instantiation-based approaches.

The relation between (a fragment of) assumption-based argumentation (ABA) and logic programs (LPs) under stable model semantics is well-studied. However, for obtaining this relation, the ABA framework needs to be restricted to being flat, i.e., a fragment where the (defeasible) assumptions can never be entailed, only assumed to be true or false. Here, we remove this restriction and show a correspondence between non-flat ABA and LPs with negation as failure in their head. We then extend this result to so-called set-stable ABA semantics, originally defined for the fragment of non-flat ABA called bipolar ABA. We showcase how to define set-stable semantics for LPs with negation as failure in their head and show the correspondence to set-stable ABA semantics.

Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or value function scores) that potentially lead to suboptimal or even distracting subgoals, preventing us from finding longer proofs. To address this challenge, we propose POETRY (PrOvE Theorems RecursivelY), which proves theorems in a recursive, level-by-level manner in the Isabelle theorem prover. Unlike previous step-by-step methods, POETRY searches for a verifiable sketch of the proof at each level and focuses on solving the current level's theorem or conjecture. Detailed proofs of intermediate conjectures within the sketch are temporarily replaced by a placeholder tactic called sorry, deferring their proofs to subsequent levels. This approach allows the theorem to be tackled incrementally by outlining the overall theorem at the first level and then solving the intermediate conjectures at deeper levels. Experiments are conducted on the miniF2F and PISA datasets and significant performance gains are observed in our POETRY approach over state-of-the-art methods. POETRY on miniF2F achieves an average proving success rate improvement of 5.1%. Moreover, we observe a substantial increase in the maximum proof length found by POETRY, from 10 to 26.

The present paper is devoted to study the effect of connected and disconnected rotations of G\"odel algebras with operators grounded on directly indecomposable structures. The structures resulting from this construction we will present are nilpotent minimum (with or without negation fixpoint, depending on whether the rotation is connected or disconnected) with special modal operators defined on a directly indecomposable algebra. In this paper we will present a (quasi-)equational definition of these latter structures. Our main results show that directly indecomposable nilpotent minimum algebras (with or without negation fixpoint) with modal operators are fully characterized as connected and disconnected rotations of directly indecomposable G\"odel algebras endowed with modal operators.

The integration of cyber-physical systems (CPS) into everyday life raises the critical necessity of ensuring their safety and reliability. An important step in this direction is requirement mining, i.e. inferring formally specified system properties from observed behaviors, in order to discover knowledge about the system. Signal Temporal Logic (STL) offers a concise yet expressive language for specifying requirements, particularly suited for CPS, where behaviors are typically represented as time series data. This work addresses the task of learning STL requirements from observed behaviors in a data-driven manner, focusing on binary classification, i.e. on inferring properties of the system which are able to discriminate between regular and anomalous behaviour, and that can be used both as classifiers and as monitors of the compliance of the CPS to desirable specifications. We present a novel framework that combines Bayesian Optimization (BO) and Information Retrieval (IR) techniques to simultaneously learn both the structure and the parameters of STL formulae, without restrictions on the STL grammar. Specifically, we propose a framework that leverages a dense vector database containing semantic-preserving continuous representations of millions of formulae, queried for facilitating the mining of requirements inside a BO loop. We demonstrate the effectiveness of our approach in several signal classification applications, showing its ability to extract interpretable insights from system executions and advance the state-of-the-art in requirement mining for CPS.

For algorithms is a longstanding challenge in Artificial Intelligence. Despite example in STL one can state properties like "the temperature of the the recognized importance of this task, a notable gap exists due room will reach 25 degrees within the next 10 minutes and will stay to the discreteness of symbolic representations and the continuous above 22 degrees for the next hour". In this area, one is typically interested nature of machine-learning computations. One of the desired bridges in understanding or verifying which properties the system between these two worlds would be to define semantically grounded under analysis is compliant to (or more precisely, in the probability vector representation (feature embedding) of logic formulae, thus enabling of observing behaviour satisfying the property). Such analysis is often to perform continuous learning and optimization in the semantic tackled by formal methods, via algorithms belonging to the world space of formulae. We tackle this goal for knowledge expressed in of quantitative model checking [4]. Signal Temporal Logic (STL) and devise a method to compute continuous In this work, we address the challenge of incorporating knowledge embeddings of formulae with several desirable properties: the in the form of temporal logic formulae inside data-driven embedding (i) is finite-dimensional, (ii) faithfully reflects the semantics learning algorithms. The key step is to devise a finite-dimensional of the formulae, (iii) does not require any learning but instead is embedding (feature mapping) of logical formulae into continuous defined from basic principles, (iv) is interpretable.