Related papers: Behavioural Preorders via Graded Monads
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
This work explores the integration of ontology-based reasoning and Machine Learning techniques for explainable value classification. By relying on an ontological formalization of moral values as in the Moral Foundations Theory, relying on…
A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a symmetric monoidal category together with an all-object-including symmetric monoidal subcategory. We think of the morphisms of this category as processes, and the…
We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
The logical parallelism of propositional connectives and type constructors extends beyond the static realm of predicates, to the dynamic realm of processes. Understanding the logical parallelism of process propositions and dynamic types was…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this paper, we connect some ideas from…
We give a leisurely introduction to our abstract framework for operational semantics based on cellular monads on transition categories. Furthermore, we relate it for the first time to an existing format, by showing that all Positive GSOS…
Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality…
For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We…
This paper proposes a way to effectively compare the potential of processes to cause conflict. In discrete event systems theory, two concurrent systems are said to be in conflict if they can get trapped in a situation where they are both…
Multi-modal methods establish comprehensive superiority over uni-modal methods. However, the imbalanced contributions of different modalities to task-dependent predictions constantly degrade the discriminative performance of canonical…
We show that streams and lazy data structures are a natural idiom for programming with infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes, jump processes, Dirichlet processes, and Beta processes. The crucial…
Motivated by applications in modelling quantum systems using coalgebraic techniques, we introduce a fibred coalgebraic logic. Our approach extends the conventional predicate lifting semantics with additional modalities relating conditions…
The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often…
Measurable cones, with linear and measurable functions as morphisms, are a model of intuitionistic linear logic and of call-by-name probabilistic PCF which accommodates "continuous data types" such as the real line. So far however, they…
We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more…
A point process on a space is a random bag of elements of that space. In this paper we explore programming with point processes in a monadic style. To this end we identify point processes on a space X with probability measures of bags of…