Related papers: On the Expressive Power of Multiple Heads in CHR

Several techniques and tools have been developed for verification of properties expressed as Horn clauses with constraints over a background theory (CHC). Current CHC verification tools implement intricate algorithms and are often limited…

Constrained Reinforcement Learning (CRL) is a subset of machine learning that introduces constraints into the traditional reinforcement learning (RL) framework. Unlike conventional RL which aims solely to maximize cumulative rewards, CRL…

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but…

Chain-of-Thought (CoT) prompting has demonstrably enhanced the performance of Large Language Models on tasks requiring multi-step inference. This success has led to widespread claims of emergent reasoning capabilities in these models. In…

This paper investigates the relationship between the Logical Algorithms language (LA) of Ganzinger and McAllester and Constraint Handling Rules (CHR). We present a translation schema from LA to CHR-rp: CHR with rule priorities, and show…

Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power. However, our understanding of the inner workings and conditions of apparition of CoT capabilities…

We address the problem of checking the satisfiability of a set of constrained Horn clauses (CHCs) possibly including more than one query. We propose a transformation technique that takes as input a set of CHCs, including a set of queries,…

The performance of modern language models (LMs) has been improved by chain-of-thought (CoT) reasoning, i.e., the process of generating intermediate results that guide the model towards a final answer. A possible explanation for this…

Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…

Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…

Concurrent Constraint Programming (CCP) is a simple and powerful model for concurrency where agents interact by telling and asking constraints. Since their inception, CCP-languages have been designed for having a strong connection to logic.…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…

Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (such as functional correctness). Hoare logic has been…

This paper presents the constrained Hybrid Metaheuristic (cHM) algorithm as a general framework for continuous optimisation. Unlike many existing metaheuristics that are tailored to specific function classes or problem domains, cHM is…

We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…

CLP(H) is an instantiation of the general constraint logic programming scheme with the constraint domain of hedges. Hedges are finite sequences of unranked terms, built over variadic function symbols and three kinds of variables: for terms,…

Large language models can exhibit emergent reasoning behaviors, often manifested as recurring lexical patterns (e.g., "wait," indicating verification). However, complex reasoning trajectories remain sparse in unconstrained sampling, and…

A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…

The reasoning abilities of Large Language Models (LLMs) can be improved by structurally denoising their weights, yet existing techniques primarily focus on denoising the feed-forward network (FFN) of the transformer block, and can not…