Related papers: L-Recursion and a new Logic for Logarithmic Space

It is a celebrated result of McKinsey and Tarski [28] that S4 is the logic of the closure algebra X+ over any dense-in-itself separable metrizable space. In particular, S4 is the logic of the closure algebra over the reals R, the rationals…

Large language models can exhibit emergent reasoning behaviors, often manifested as recurring lexical patterns (e.g., "wait," indicating verification). However, complex reasoning trajectories remain sparse in unconstrained sampling, and…

It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…

We introduce infinitary action logic with exponentiation -- that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules…

Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive…

We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…

Logically constrained term rewriting systems (LCTRSs) are a program analyzing formalism with native support for data types which are not (co)inductively defined. As a first-order formalism, LCTRSs have accommodated only analysis of…

Large language models (LLMs) have rapidly progressed into general-purpose agents capable of solving a broad spectrum of tasks. However, current models remain inefficient at reasoning: they apply fixed inference-time compute regardless of…

We study Boolean classification problems over relational background structures in the logical framework introduced by Grohe and Tur\'an (TOCS 2004). It is known (Grohe and Ritzert, LICS 2017) that classifiers definable in first-order logic…

Reasoning language models such as DeepSeek-R1 produce long chain-of-thought traces during inference time which make them costly to deploy at scale. We show that using compression techniques such as neural network pruning produces greater…

Effective light cones, characterized by Lieb-Robinson bounds, emerge in nonrelativistic local quantum systems. Here, we present several analytical results derived from logarithmic light cones (LLCs). Possible origins of LLCs include the…

In this paper, we develop a quantified propositional proof systems that corresponds to logarithmic-space reasoning. We begin by defining a class SigmaCNF(2) of quantified formulas that can be evaluated in log space. Then our new proof…

We characterize the expressive power of description logic (DL) TBoxes, both for expressive DLs such as ALC and ALCQIO and lightweight DLs such as DL-Lite and EL. Our characterizations are relative to first-order logic, based on a wide range…

Chain-of-Thought (CoT) reasoning enhances large language models (LLMs) by enabling step-by-step problem-solving, yet its extension to Long-CoT introduces substantial computational overhead due to increased token length. Existing compression…

Log parsing transforms log messages into structured formats, serving as the prerequisite step for various log analysis tasks. Although a variety of log parsing approaches have been proposed, their performance on complicated log data remains…

In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…

Large Language Models (LLMs), despite their remarkable capabilities, rely on singular, pre-dominant reasoning paradigms, hindering their performance on intricate problems that demand diverse cognitive strategies. To address this, we…

We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model…

In the logical framework introduced by Grohe and Tur\'an (TOCS 2004) for Boolean classification problems, the instances to classify are tuples from a logical structure, and Boolean classifiers are described by parametric models based on…

The recursive logit (RL) model provides a flexible framework for modeling sequential decision-making in transportation and choice networks, with important applications in route choice analysis, multiple discrete choice problems, and…