Related papers: SCL(EQ): SCL for First-Order Logic with Equality

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

Contrastive learning is an efficient approach to self-supervised representation learning. Although recent studies have made progress in the theoretical understanding of contrastive learning, the investigation of how to characterize the…

The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…

In this work, a new class of stochastic gradient algorithm is developed based on $q$-calculus. Unlike the existing $q$-LMS algorithm, the proposed approach fully utilizes the concept of $q$-calculus by incorporating time-varying $q$…

Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…

We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…

In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…

Neural networks exhibit severe brittleness to semantically irrelevant transformations. A mere 75ms electrocardiogram (ECG) phase shift degrades latent cosine similarity from 1.0 to 0.2, while sensor rotations collapse activity recognition…

In this article we consider the Conditional Super Learner (CSL), an algorithm which selects the best model candidate from a library conditional on the covariates. The CSL expands the idea of using cross-validation to select the best model…

Continual learning (CL) is a learning paradigm that emulates the human capability of learning and accumulating knowledge continually without forgetting the previously learned knowledge and also transferring the learned knowledge to help…

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

Large language models have advanced natural language understanding and generation, but their use as autonomous agents introduces architectural challenges for multi-step tasks. Existing frameworks often mix cognition, memory, and control in…

Three-valued conditional logic (CL) is defined by Guzm\'an and Squier (1990), and based on McCarthy's noncommutative connectives, axiomatises a short-circuit logic (SCL) that defines more identities than three-valued MSCL (Memorising SCL,…

In-context learning (ICL) has emerged as a successful paradigm for leveraging large language models (LLMs). However, it often struggles to generalize beyond the distribution of the provided demonstrations. A recent advancement in enhancing…

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its…

Semi-supervised continual learning (SSCL) seeks to leverage both labeled and unlabeled data in a sequential learning setup, aiming to reduce annotation costs while managing continual data arrival. SSCL introduces complex challenges,…

We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…