Related papers: L-Recursion and a new Logic for Logarithmic Space
We introduce a description logic ALCQIO_{b,Re} which adds reachability assertions to ALCQIO, a sub-logic of the two-variable fragment of first order logic with counting quantifiers. ALCQIO_{b,Re} is well-suited for applications in software…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist such a…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
The rapid emergence of new entities -- driven by cultural shifts, evolving trends, and personalized user data -- poses a significant challenge for existing Speech Large Language Models (Speech LLMs). While these models excel at general…
Large language models (LLMs) have achieved remarkable multi-step reasoning capabilities across various domains. However, LLMs still face distinct challenges in complex logical reasoning, as (1) proof-finding requires systematic exploration…
A catalytic machine is a model of computation where a traditional space-bounded machine is augmented with an additional, significantly larger, "catalytic" tape, which, while being available as a work tape, has the caveat of being…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…
Hypertrace logic is a sorted first-order logic with separate sorts for time and execution traces. Its formulas specify hyperproperties, which are properties relating multiple traces. In this work, we extend hypertrace logic by introducing…
Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…
We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which enhances the safety properties of programs, but also supports…
Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP,…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
In this paper, we discuss an algorithm for the problem of undirected st-connectivity that is deterministic and log-space, namely that of Reingold within his 2008 paper "Undirected Connectivity in Log-Space". We further present a separate…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
We present quantitative logics with two-step semantics based on the framework of quantitative logics introduced by Arenas et al. (2020) and the two-step semantics defined in the context of weighted logics by Gastin & Monmege (2018). We show…
We consider an extension of linear-time temporal logic (LTL) with both local and remote data constraints interpreted over a concrete domain. This extension is a natural extension of constraint LTL and the Temporal Logic of Repeating Values,…
We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of…
Evaluating LLM reliability via scalar probabilities often fails to capture the structural dynamics of reasoning. We introduce TRACED, a framework that assesses reasoning quality through theoretically grounded geometric kinematics. By…