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We investigate algebraic and topological semantics of the modal logic S4CI and obtain strong completeness of the given system in the case of local semantic consequence relations. In addition, we consider an extension of the logic S4CI with…
We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
Word embeddings have demonstrated strong performance on NLP tasks. However, lack of interpretability and the unsupervised nature of word embeddings have limited their use within computational social science and digital humanities. We…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
The performance of Large language models (LLMs) across a broad range of domains has been impressive but have been critiqued as not being able to reason about their process and conclusions derived. This is to explain the conclusions draw,…
Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…
While pre-trained language models (LMs) have brought great improvements in many NLP tasks, there is increasing attention to explore capabilities of LMs and interpret their predictions. However, existing works usually focus only on a certain…
Results of computational complexity exist for a wide range of phrase structure-based grammar formalisms, while there is an apparent lack of such results for dependency-based formalisms. We here adapt a result on the complexity of…
The linguistic applications of the Lambek calculus suggest its semantics over algebras of formal languages. A straightforward approach to construct such semantics indeed yields a brilliant completeness theorem (Pentus 1995). However,…
To interpret deep models' predictions, attention-based visual cues are widely used in addressing \textit{why} deep models make such predictions. Beyond that, the current research community becomes more interested in reasoning \textit{how}…
As large language models (LLMs) excel at code reasoning, a natural question arises: can an LLM execute programs (i.e., act as an interpreter) purely based on a programming language's formal semantics? If so, it will enable rapid prototyping…
We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus (specifically: every analytic structural rule…
We present a general relational semantics framework which, by varying the axiomatization and components of the relational structures, provides a uniform semantics for sentential logics, classical and non-classical alike. The approach we…
In-context learning (ICL) has emerged as a successful paradigm for leveraging large language models (LLMs). However, it often struggles to generalize beyond the distribution of the provided demonstrations. A recent advancement in enhancing…
Joint intent detection and slot filling, which is also termed as joint NLU (Natural Language Understanding) is invaluable for smart voice assistants. Recent advancements in this area have been heavily focusing on improving accuracy using…
We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
Computation Tree Logic (CTL) and its extensions CTL* and CTL+ are widely used in automated verification as a basis for common model checking tools. But while they can express many properties of interest like reachability, even simple…