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Bealer's intensional logics T1 and T2 were proposed and expounded most fully in his book \emph{Quality and Concept} (1982) \cite{QC} as well in \cite{C}. These logics are unique in being extensions of classical first-order associated to a…
We provide a rough sets semantics for the three-valued extension of first-order Priest's da Costa logic, which we studied in [Castiglioni, J.L. and Ertola-Biraben, R.C. Modalities combining two negations. {\em Journal of Logic and…
This paper presents a complete decision procedure for the entire quantifier-free fragment of Separation Logic ($\seplog$) interpreted over heaplets with data elements ranging over a parametric multi-sorted (possibly infinite) domain. The…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
Large language models (LLMs) has experienced exponential growth, they demonstrate remarkable performance across various tasks. Notwithstanding, contemporary research primarily centers on enhancing the size and quality of pretraining data,…
Temporal Logic (TL), especially Signal Temporal Logic (STL), enables precise formal specification, making it widely used in cyber-physical systems such as autonomous driving and robotics. Automatically transforming NL into STL is an…
Text simplification (TS) aims to reduce the lexical and structural complexity of a text, while still retaining the semantic meaning. Current automatic TS techniques are limited to either lexical-level applications or manually defining a…
Deep reinforcement learning (RL) methods often require many trials before convergence, and no direct interpretability of trained policies is provided. In order to achieve fast convergence and interpretability for the policy in RL, we…
We introduce the first order logic of proofs $FOLP^\Box$ in the joint language combining justification terms and binding modalities. The main issue is Kripke--style semantics for this logic. We describe models for $FOLP^\Box$ in terms of…
In this work we develop a fully automatic verification procedure of safety properties of Scade programs. We transform each such program into an SMT instance (Satisfiability Modulo Theories) and feed this to a solver. The goal is to have a…
Sign Language Translation (SLT) first uses a Sign Language Recognition (SLR) system to extract sign language glosses from videos. Then, a translation system generates spoken language translations from the sign language glosses. This paper…
Recent years have witnessed the rapid advance in neural machine translation (NMT), the core of which lies in the encoder-decoder architecture. Inspired by the recent progress of large-scale pre-trained language models on machine translation…
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
Predicting the judgment of a legal case from its unannotated case facts is a challenging task. The lengthy and non-uniform document structure poses an even greater challenge in extracting information for decision prediction. In this work,…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
In the last few years there have been rapid developments in SMT solving for finite fields. These include new decision procedures, new implementations of SMT theory solvers, and new software verifiers that rely on SMT solving for finite…
We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…
In this paper we give automata-based representation of LTL-FO$^+$ properties. LTL-FO$^+$ is an extension of LTL that includes first-order quantification over bounded variable, thus greatly increasing the expressivity of the language. An…