Related papers: Foundational Extensible Corecursion
Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
In previous work we developed a framework of computational models for the concurrent execution of functions on different levels of abstraction. It shows that the traditional sequential execution of function is just a possible implementation…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
A protocol-independent secrecy theorem is established and applied to several non-trivial protocols. In particular, it is applied to protocols proposed for protecting the computation results of free-roaming mobile agents doing comparison…
Large language models (LLMs) have advanced general-purpose reasoning, showing strong performance across diverse tasks. However, existing methods often rely on implicit exploration, where the model follows stochastic and unguided reasoning…
We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal…
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
Refinement type checkers are a powerful way to reason about functional programs. For example, one can prove properties of a slow, specification implementation, porting the proofs to an optimized implementation that behaves the same. Without…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
The trustworthiness of AI decision-making systems is increasingly important. A key feature of such systems is the ability to provide recommendations for how an individual may reverse a negative decision, a problem known as algorithmic…
Explainability of a classification model is crucial when deployed in real-world decision support systems. Explanations make predictions actionable to the user and should inform about the capabilities and limitations of the system. Existing…
Large language models show improved downstream task performance when prompted to generate step-by-step reasoning to justify their final answers. These reasoning steps greatly improve model interpretability and verification, but objectively…
Intensionality is a phenomenon that occurs in logic and computation. In the most general sense, a function is intensional if it operates at a level finer than (extensional) equality. This is a familiar setting for computer scientists, who…
We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…
Obfuscation of computer programs has historically been approached either as a practical but \textit{ad hoc} craft to make reverse engineering subjectively difficult, or as a sound theoretical investigation unfortunately detached from the…