Related papers: A Simple Soundness Proof for Dependent Object Type…
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…
Recent advancements in multimodal reasoning have largely overlooked the audio modality. We introduce Audio-Reasoner, a large-scale audio language model for deep reasoning in audio tasks. We meticulously curated a large-scale and diverse…
This work provides a study to demonstrate the potential of using off-the-shelf programming languages and their theories to build sound language-based-security tools. Our study focuses on information flow security encompassing…
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want…
Pixel-wise prediction with deep neural network has become an effective paradigm for salient object detection (SOD) and achieved remarkable performance. However, very few SOD models are robust against adversarial attacks which are visually…
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…
This work studies gradual typing for row types and row polymorphism. Key ingredients in this work are the dynamic row type, which represents a statically unknown part of a row, and consistency for row types, which allows injecting static…
Chain-of-thought (CoT) prompting is a de-facto standard technique to elicit reasoning-like responses from large language models (LLMs), allowing them to spell out individual steps before giving a final answer. While the resemblance to…
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…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Task oriented language understanding in dialog systems is often modeled using intents (task of a query) and slots (parameters for that task). Intent detection and slot tagging are, in turn, modeled using sentence classification and word…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
Dedukti is a Logical Framework based on the $\lambda$$\Pi$-Calculus Modulo Theory. We show that many theories can be expressed in Dedukti: constructive and classical predicate logic, Simple type theory, programming languages, Pure type…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
Logical atomicity has been widely accepted as a specification format for data structures in concurrent separation logic. While both lock-free and lock-based data structures have been verified against logically atomic specifications, most of…
Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which…