Related papers: Presentable signatures and initial semantics
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Syntax is a latent hierarchical structure which underpins the robust and compositional nature of human language. In this work, we explore the hypothesis that syntactic dependencies can be represented in language model attention…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
It is often useful, if not necessary, to reason about the syntactic structure of an expression in an interpreted language (i.e., a language with a semantics). This paper introduces a mathematical structure called a syntax framework that is…
Program synthesis--the automated generation of executable code from high-level specifications--has been a central goal of computer science for over fifty years. This thesis provides a comparative literature review of the main paradigms that…
A wide-spectrum language integrates specification constructs into a programming language in a manner that treats a specification command just like any other command. This paper investigates a semantic model for a wide-spectrum language that…
Program synthesis is the task of constructing a program conforming to a given specification. We focus on deductive synthesis, and in particular on synthesis problems with specifications given as $\forall\exists$-formulas, expressing the…
The intricate hierarchical structure of syntax is fundamental to the intricate and systematic nature of human language. This study investigates the premise that language models, specifically their attention distributions, can encapsulate…
While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
To equip SL with software properly, we need an input system to represent and manipulate signed contents in the same way that every day software allows to process written text. Refuting the claim that video is good enough a medium to serve…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
It is well-known that big-step semantics is not able to distinguish stuck and non-terminating computations. This is a strong limitation as it makes very difficult to reason about properties involving infinite computations, such as type…
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal…