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Safe reinforcement learning (RL) offers advanced solutions to constrained optimal control problems. Existing studies in safe RL implicitly assume continuity in policy functions, where policies map states to actions in a smooth,…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
Hierarchical decision problems are often modeled as bilevel programs in which a leader commits to a policy and a follower responds optimally. When the follower's optimal response is nonunique, or when only near-optimal follower behavior can…
We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason…
Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically…
We study approximate equivalence relations up to commensurability, in the presence of a definable measure. As a basic framework, we give a presentation of probability logic based on continuous logic. Hoover's normal form is valid here; if…
The deployment of Large Vision-Language Models (LVLMs) for real-world document question answering is often constrained by dynamic, user-defined policies that dictate information disclosure based on context. While ensuring adherence to these…
Bipartite data is common in data engineering and brings unique challenges, particularly when it comes to clustering tasks that impose on strong structural assumptions. This work presents an unsupervised method for assessing similarity in…
Weighted bipolar argumentation frameworks offer a tool for decision support and social media analysis. Arguments are evaluated by an iterative procedure that takes initial weights and attack and support relations into account. Until…
Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…
We present a comprehensive view of the relations among several privacy notions: differential privacy (DP) [1], Bayesian differential privacy (BDP) [2], semantic privacy (SP) [3], and membership privacy (MP) [4]. The results are organized…
High-dimensional categorical data arise in diverse scientific domains and are often accompanied by covariates. Latent class regression models are routinely used in such settings, reducing dimensionality by assuming conditional independence…
The generalized Hopf (Bautin) bifurcation is a well-studied codimension two bifurcation characterized by an equilibrium with a pair of simple purely imaginary eigenvalues as the only critical eigenvalues and the vanishing first Lyapunov…
Automated Theorem Proving (ATP) represents a fundamental challenge in Artificial Intelligence (AI), requiring the construction of machine-verifiable proofs in formal languages such as Lean to evaluate AI reasoning capabilities.…
This paper develops an interpretive framework for divergence P-values and S-values within a descriptive frequentist perspective. Statistical analysis is framed as operating within idealized worlds defined by a set of assumptions and a…
Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…
This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter…
We devise two complementary characterizations of hereditary history-preserving bisimilarity (HHPB): a denotational one, based on stable configuration structures, and an operational one, formulated in a reversible process calculus. Our…
Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…