Related papers: Local Local Reasoning: A BI-Hyperdoctrine for Full…

Separation logic is used to reason locally about stateful programs. State of the art program logics for higher-order store are usually built on top of untyped operational semantics, in part because traditional denotational methods have…

Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…

We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and…

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…

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…

The logic of bunched implications (BI) is a substructural logic that forms the backbone of separation logic, the much studied logic for reasoning about heap-manipulating programs. Although the proof theory and metatheory of BI are…

We present a denotational account of dynamic allocation of potentially cyclic memory cells using a monad on a functor category. We identify the collection of heaps as an object in a different functor category equipped with a monad for…

It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…

Multi-step reasoning remains a central challenge for large language models: single-pass generation is efficient but lacks accuracy; tree-search methods explore multiple paths but are computation-heavy. We address this gap by distilling…

In modern machine learning, pattern recognition replaces realtime semantic reasoning. The mapping from input to output is learned with fixed semantics by training outcomes deliberately. This is an expensive and static approach which depends…

We propose a formal model of reasoning limitations in large neural net models for language, grounded in the depth of their neural architecture. By treating neural networks as linear operators over logic predicate space we show that each…

Case-based reasoning (CBR) as a methodology for problem-solving can use any appropriate computational technique. This position paper argues that CBR researchers have somewhat overlooked recent developments in deep learning and large…

Matching natural language sentences is central for many applications such as information retrieval and question answering. Existing deep models rely on a single sentence representation or multiple granularity representations for matching.…

Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…

We present Classical BI (CBI), a new addition to the family of bunched logics which originates in O'Hearn and Pym's logic of bunched implications BI. CBI differs from existing bunched logics in that its multiplicative connectives behave…

Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…

Large language models often expose their brittleness in reasoning tasks, especially while executing long chains of reasoning over context. We propose MemReasoner, a new and simple memory-augmented LLM architecture, in which the memory…

Compositional generalization remains a foundational weakness of modern neural networks, limiting their robustness and applicability in domains requiring out-of-distribution reasoning. A central, yet unverified, assumption in neuro-symbolic…

Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute…