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GQL has recently emerged as the standard query language over graph databases (particularly, the property graph model). Indeed, this is analogous to the role of SQL for relational databases. Unlike SQL, however, fundamental problems…

We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…

Grounded claim factuality checking is important for large language model (LLM) applications such as retrieval-augmented generation, as it helps users assess the correctness of generated outputs. Existing metrics using entailment classifiers…

Clinical diagnosis of stuttering requires an assessment by a licensed speech-language pathologist. However, this process is time-consuming and requires clinicians with training and experience in stuttering and fluency disorders.…

We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of…

To reduce issues like hallucinations and lack of control in Large Language Models (LLMs), a common method is to generate responses by grounding on external contexts given as input, known as knowledge-augmented models. However, previous…

Since the topic emerged several years ago, work on regular model checking has mostly been devoted to the verification of state reachability and safety properties. Though it was known that linear temporal properties could also be checked…

Large language models (LLMs) such as GPT-3 and GPT-4 are powerful but their weights are often publicly unavailable and their immense sizes make the models difficult to be tuned with common hardware. As a result, effectively tuning these…

We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $\mc{NP}$-complete; for $L$ of height at…

We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…

Recent studies have used both automatic metrics and human evaluations to assess the simplification abilities of LLMs. However, the suitability of existing evaluation methodologies for LLMs remains in question. First, the suitability of…

While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem…

Constant-rate multi-mode systems (MMS) are hybrid systems with finitely many modes and real-valued variables that evolve over continuous time according to mode-specific constant rates. We introduce a variant of linear temporal logic (LTL)…

Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…

We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…

For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…

Language models (LMs), despite their advances, often depend on spurious correlations, undermining their accuracy and generalizability. This study addresses the overlooked impact of subtler, more complex shortcuts that compromise model…

Surprisal theory posits that the processing difficulty of a word is determined by its predictability in context, offering a potential link between human sentence processing and next-word predictions from language models. While language…

Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…