Related papers: SCL(FOL) Revisited
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…
We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…
Training expert LLMs in domains with scarce data is difficult, often relying on multiple-choice questions (MCQs). However, standard outcome-based reinforcement learning (RL) on MCQs is risky. While it may improve accuracy, we observe it…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of…
Despite the conceptual simplicity of sequential consistency (SC), the semantics of SC atomic operations and fences in the C11 and OpenCL memory models is subtle, leading to convoluted prose descriptions that translate to complex axiomatic…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
First-Order Logic (FOL), also called first-order predicate calculus, is a formal language that provides a framework to comprehensively represent a world and its present state, including all of its entities, attributes, and complex…
We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…
In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically…
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We present a hypersequent calculus $\text{G}^3\text{\L}\forall$ for first-order infinite-valued {\L}ukasiewicz logic and for an extension of it, first-order rational Pavelka logic; the calculus is intended for bottom-up proof search. In…
This paper proposes a new logic RoCTL* to model robustness in concurrent systems. RoCTL* extends CTL* with the addition of Obligatory and Robustly operators, which quantify over failure-free paths and paths with one more failure…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…
Continual Learning (CL) aims to train neural networks on a dynamic stream of tasks without forgetting previously learned knowledge. Among optimization-based approaches, C-Flat has emerged as a promising solution due to its plug-and-play…
Self-supervised learning (SSL) is able to build latent representations that generalize well to unseen data. However, only a few SSL techniques exist for the online CL setting, where data arrives in small minibatches, the model must comply…