Related papers: Nested Refinements for Dynamic Languages
Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…
To appear in Theory and Practice of Logic Programming (TPLP). Dynamic systems play a central role in fields such as planning, verification, and databases. Fragmented throughout these fields, we find a multitude of languages to formally…
This article describes a very high-level language for clear description of distributed algorithms and optimizations necessary for generating efficient implementations. The language supports high-level control flows where complex…
Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…
Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…
In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…
There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing…
Relational type systems have been designed for several applications including information flow, differential privacy, and cost analysis. In order to achieve the best results, these systems often use relational refinements and relational…
This paper addresses the problems of missing reasoning chains and insufficient entity-level semantic understanding in large language models when dealing with tasks that require structured knowledge. It proposes a fine-tuning algorithm…
Software synthesis - the process of generating complete, general-purpose programs from specifications - has become a hot research topic in the past few years. For decades the problem was thought to be insurmountable: the search space of…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
We present {\lambda}ert, a type theory supporting refinement types with explicit proofs. Instead of solving refinement constraints with an SMT solver like DML and Liquid Haskell, our system requires and permits programmers to embed proofs…
In paper describes the new logic programming language Delta, which have a many good properties. Delta-programs is p-computable, verifiable and can translation on other languages. Also we describe the Delta-methodology for constructing…
Large language models excel on static benchmarks, but their ability as self-learning agents in dynamic environments remains unclear. We evaluate three prompting strategies: self-reflection, heuristic mutation, and planning across dynamic…
Driven by expressiveness commonalities of Python and our Python-based embedded logic-based language Natlog, we design high-level interaction patterns between equivalent language constructs and data types on the two sides. By directly…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…