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Language models' (LMs) proficiency in handling deterministic symbolic reasoning and rule-based tasks remains limited due to their dependency implicit learning on textual data. To endow LMs with genuine rule comprehension abilities, we…

Nowadays, numerous services based on large-scale distributed systems have been developed to boost the convenience of human life. On the other side, it becomes a significant challenge to ensure the correctness and properties of these systems…

Sequential recommender systems have achieved significant success in modeling temporal user behavior but remain limited in capturing rich user semantics beyond interaction patterns. Large Language Models (LLMs) present opportunities to…

Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…

This paper develops stable canonical rules for intuitionistic modal logics, which were first introduced for superintuitionistic logics and transitive nor mal modal logics in [1] and [2] respectively. We first prove that every in…

Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…

Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…

Prior methods to text segmentation are mostly at token level. Despite the adequacy, this nature limits their full potential to capture the long-term dependencies among segments. In this work, we propose a novel framework that incrementally…

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…

The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of…

We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…

Large language models (LLMs) have revolutionized natural language processing (NLP) by excelling at understanding and generating human-like text. However, their widespread deployment can be prohibitively expensive. SortedNet is a recent…

Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…

Past work probing compositionality in sentence embedding models faces issues determining the causal impact of implicit syntax representations. Given a sentence, we construct a neural module net based on its syntax parse and train it…

We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…

Natural language is hierarchically structured: smaller units (e.g., phrases) are nested within larger units (e.g., clauses). When a larger constituent ends, all of the smaller constituents that are nested within it must also be closed.…

Although neural sequence-to-sequence models have been successfully applied to semantic parsing, they fail at compositional generalization, i.e., they are unable to systematically generalize to unseen compositions of seen components.…

Programming or scripting languages used in real-world systems are seldom designed with a formal semantics in mind from the outset. Therefore, developing well-founded analysis tools for these systems requires reverse-engineering a formal…

We give a procedure for translating geometric Kripke frame axioms into structural hypersequent rules for the corresponding intermediate logics in Int^*/Geo that admit weakening, contraction and in some cases, cut. We give a procedure for…

Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…