Related papers: A Coq Library of Sets for Teaching Denotational Se…
The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
In this work, we investigate whether improving task clarity can enhance reasoning ability of large language models, focusing on theorem proving in Coq. We introduce a concept-level metric to evaluate task clarity and show that adding…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
This paper presents a method for semantic indexing and describes its application in the field of knowledge representation. Starting point of the semantic indexing is the knowledge represented by concept hierarchies. The goal is to assign…
Context-free grammar simplification is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of the fact that…
Semantic NLP applications often rely on dependency trees to recognize major elements of the proposition structure of sentences. Yet, while much semantic structure is indeed expressed by syntax, many phenomena are not easily read out of…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Large language models have made significant advancements in various natural language processing tasks, including coreference resolution. However, traditional methods often fall short in effectively distinguishing referential relationships…
Learning to fuse vision and language information and representing them is an important research problem with many applications. Recent progresses have leveraged the ideas of pre-training (from language modeling) and attention layers in…
Applications like program synthesis sometimes require proving that a property holds for all of the infinitely many programs described by a grammar - i.e., an inductively defined set of programs. Current verification frameworks…
Knowledge graphs represent real-world entities and their relations in a semantically-rich structure supported by ontologies. Exploring this data with machine learning methods often relies on knowledge graph embeddings, which produce latent…
The basics of set theory are usually copied, directly or indirectly, by computer scientists from introductions to mathematical texts. Often mathematicians are content with special cases when the general case is of no mathematical interest.…
SQL is the world's most popular declarative language, forming the basis of the multi-billion-dollar database industry. Although SQL has been standardized, the full standard is based on ambiguous natural language rather than formal…
Successfully modeling state and analytics-based semantic relationships of documents enhances representation, importance, relevancy, provenience, and priority of the document. These attributes are the core elements that form the…
Learning representations for semantic relations is important for various tasks such as analogy detection, relational search, and relation classification. Although there have been several proposals for learning representations for individual…
In the paper a new programming construct, called concept, is introduced. Concept is pair of two classes: a reference class and an object class. Instances of the reference classes are passed-by-value and are intended to represent objects.…
A core problem in learning semantic parsers from denotations is picking out consistent logical forms--those that yield the correct denotation--from a combinatorially large space. To control the search space, previous work relied on…