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

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…

We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely…

Unsupervised clustering aims at discovering the semantic categories of data according to some distance measured in the representation space. However, different categories often overlap with each other in the representation space at the…

We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a…

The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…

In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on…

In Continual Learning (CL), a neural network is trained on a stream of data whose distribution changes over time. In this context, the main problem is how to learn new information without forgetting old knowledge (i.e., Catastrophic…

Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…

We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…

Consequence-based calculi are a family of reasoning algorithms for description logics (DLs), and they combine hypertableau and resolution in a way that often achieves excellent performance in practice. Up to now, however, they were proposed…

It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…

Session-based recommendation, which aims to predict the next item of users' interest as per an existing sequence interaction of items, has attracted growing applications of Contrastive Learning (CL) with improved user and item…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

Quantum logic (QL) is a non-classical logic for analyzing the propositions of quantum physics. Modal logic MB, which is a logic that handles the value of the inner product that appears in quantum mechanics, was constructed with the…

Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend…

In-context learning (ICL) allows some autoregressive models to solve tasks via next-token prediction and without needing further training. This has led to claims about these model's ability to solve (learn) unseen tasks with only a few…

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…

Self-supervised contrastive learning (CL) has achieved remarkable empirical success, often producing representations that rival supervised pre-training on downstream tasks. Recent theory explains this by showing that the CL loss closely…

We recently proposed Acceleration Driven Clause Learning (ADCL), a novel calculus to analyze satisfiability of Constrained Horn Clauses (CHCs). Here, we adapt ADCL to transition systems and introduce ADCL-NT, a variant for disproving…