Related papers: On LL(k) linear conjunctive grammars
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more…
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed $\lambda$-terms, defined using denotational…
Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…
Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…
We introduce Transformer Grammars (TGs), a novel class of Transformer language models that combine (i) the expressive power, scalability, and strong performance of Transformers and (ii) recursive syntactic compositions, which here are…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
The heterogeneity of tools that support temporal logic formulae poses several challenges in terms of interoperability. In particular, a standard syntax for temporal logic on finite traces, despite similar to the one for infinite traces, is…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
The language of modal logic is capable of expressing first-order conditions on Kripke frames. The classic result by Henrik Sahlqvist identifies a significant class of modal formulas for which first-order conditions -- or Sahlqvist…
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…
Building causal graphs can be a laborious process. To ensure all relevant causal pathways have been captured, researchers often have to discuss with clinicians and experts while also reviewing extensive relevant medical literature. By…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
A structural time series model additively decomposes into generative, semantically-meaningful components, each of which depends on a vector of parameters. We demonstrate that considering each generative component together with its vector of…
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…
Futrell and Mahowald (2025) frame the success of neural language models (LMs) as supporting gradient, usage-based linguistic theories. I argue that LMs can also instantiate theories based on formal structures - the types of theories seen in…
A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism---to express syntactic theories purely in terms of the properties of…
Large language models (LLMs) have significantly advanced performance across a spectrum of natural language processing (NLP) tasks. Yet, their application to knowledge graphs (KGs), which describe facts in the form of triplets and allow…