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Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…

Compositional generalization is a crucial property in artificial intelligence, enabling models to handle novel combinations of known components. While most deep learning models lack this capability, certain models succeed in specific tasks,…

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…

Common approaches to concurrent programming begin with languages whose semantics are naturally sequential and add new constructs that provide limited access to concurrency, as exemplified by futures. This approach has been quite successful,…

To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and simplistic assumption is often violated in practice, which…

Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…

Precedential constraint is one foundation of case-based reasoning in AI and Law. It generally assumes that the underlying set of precedents must be consistent. To relax this assumption, a generalized notion of the reason model has been…

The problem of replicating the flexibility of human common-sense reasoning has captured the imagination of computer scientists since the early days of Alan Turing's foundational work on computation and the philosophy of artificial…

We study quadrangular properties of binary relations on a set $X$~--i.e., properties defined on configurations of four elements--~within an agonistic interpretation, where $xRy$ is interpreted as $x$ ``attacks''~$y$. Such relations induce a…

Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…

Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…

The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when…

We introduce Conflict-Aware Replicated Data Types (CARDs). CARDs are significantly more expressive than Conflict-free Replicated Data Types (CRDTs) as they support operations that can conflict with each other. Introducing conflicting…

Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous…

In this paper, we introduce a formal notion of partial compliance, called Attack-resistance, of a computer program running together with a defense mechanism w.r.t a non-exploitability specification. In our setting, a program may contain…

Since the birth of software engineering, it always are recognized as one pure engineering subject, therefore, the foundational scientific problems are not paid much attention. This paper proposes that Requirements Analysis, the kernel…

Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…

Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…

Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…

We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…