Related papers: On Incorrectness Logic and Kleene Algebra with Top…
A Kleene semiring is an algebraic structure satisfying the axioms of Kleene algebra, minus the annihilation axioms (x.0 = 0 = 0.x). We show that Kleene semirings (like Kleene algebras) admit the efficient elimination of various kinds of…
Logical reasoning is a critical benchmark for evaluating the capabilities of large language models (LLMs), as it reflects their ability to derive valid conclusions from given premises. While the combination of test-time scaling with…
Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team semantic constructions have been used to generate expressively enriched logics still conserving nice properties, such as compactness or decidability. In contrast,…
Chain-of-Thought (CoT) reasoning successfully enhances the reasoning capabilities of Large Language Models (LLMs), yet it incurs substantial computational overhead for inference. Existing CoT compression methods often suffer from a critical…
This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET) with the Enriched Lawvere Theories. We extend QETs to Metric…
Pretrained deep contextual representations have advanced the state-of-the-art on various commonsense NLP tasks, but we lack a concrete understanding of the capability of these models. Thus, we investigate and challenge several aspects of…
Pretrained language models, such as BERT and RoBERTa, have shown large improvements in the commonsense reasoning benchmark COPA. However, recent work found that many improvements in benchmarks of natural language understanding are not due…
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…
Large Language Models (LLMs) have shown remarkable progress across domains, yet their ability to perform inductive reasoning - inferring latent rules from sparse examples - remains limited. It is often assumed that chain-of-thought (CoT)…
Neural metrics for machine translation evaluation, such as COMET, exhibit significant improvements in their correlation with human judgments, as compared to traditional metrics based on lexical overlap, such as BLEU. Yet, neural metrics…
Multiple-choice reasoning benchmarks face dual challenges: rapid saturation from advancing models and data contamination that undermines static evaluations. Ad-hoc hardening methods (paraphrasing, perturbation) attempt to increase…
In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), a concept aimed at minimizing reliance on domain-specific knowledge, enabling more accurate evaluation of models' reasoning abilities in out-of-distribution settings. Based…
A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform…
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…
Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the…
Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two…
Abstract interpretation offers a powerful toolset for static analysis, tackling precision, complexity and state-explosion issues. In the literature, state partitioning abstractions based on (bi)simulation and property-preserving state…
We introduce weighted NetKAT, a domain-specific language for modeling and verifying quantitative network properties. The language is parametric on a semiring, enabling the treatment of a wide range of quantities in a uniform way. We provide…
Chain-of-Thought (CoT) plays a crucial role in reasoning for math problem solving. We conduct a comprehensive examination of methods for designing CoT, comparing conventional natural language CoT with various program CoTs, including the…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…