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Prompt-based fine-tuning has become an essential method for eliciting information encoded in pre-trained language models for a variety of tasks, including text classification. For multi-class classification tasks, prompt-based fine-tuning…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
Large Language Models (LLMs) often fail to utilize their latent reasoning capabilities due to a distributional mismatch between ambiguous human inquiries and the structured logic required for machine activation. Existing alignment methods…
This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…
We propose an architecture to jointly learn word and label embeddings for slot filling in spoken language understanding. The proposed approach encodes labels using a combination of word embeddings and straightforward word-label association…
In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In…
Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…
Input/Output (I/O) logic is a general framework for reasoning about conditional norms and/or causal relations. We streamline Bochman's causal I/O logics via proof-search-oriented sequent calculi. Our calculi establish a natural syntactic…
Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus. Later a deep inference system BV was developed with…
Noisy labels can negatively impact the performance of deep neural networks. One common solution is label refurbishment, which involves reconstructing noisy labels through predictions and distributions. However, these methods may introduce…
The logic of Bunched Implications (BI) freely combines additive and multiplicative connectives, including implications; however, despite its well-studied proof theory, proof-search in BI has always been a difficult problem. The focusing…
This report extends the Spectral Neuro-Symbolic Reasoning (Spectral NSR) framework by introducing three semantically grounded enhancements: (1) transformer-based node merging using contextual embeddings (e.g., Sentence-BERT, SimCSE) to…
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda…
Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…
Semantic Role Labeling (SRL) provides an explicit representation of predicate-argument structure, capturing linguistically grounded relations such as who did what to whom. While recent NLP progress has been dominated by large language…
We report our ongoing work about a new deep architecture working in tandem with a statistical test procedure for jointly training texts and their label descriptions for multi-label and multi-class classification tasks. A statistical…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…