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We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer…
We study strictly positive logics in the language $\mathscr{L}^+$, which constructs formulas from $\top$, propositional variables, conjunction, and diamond modalities. We begin with the base system $\bf K^+$, the strictly positive fragment…
Chain-of-Thought (CoT) has been shown to significantly improve the reasoning accuracy of large language models (LLMs) on complex tasks. However, due to the autoregressive, step-by-step generation paradigm, existing CoT methods suffer from…
We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$…
Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form $x\,y$ which decompose a compound data structure into its…
Two distinct algorithms are presented to extract (schemata of) resolution proofs from closed tableaux for propositional schemata. The first one handles the most efficient version of the tableau calculus but generates very complex…
This paper addresses the resilience of large-scale closed-loop structured systems in the sense of arbitrary pole placement when subject to failure of feedback links. Given a structured system with input, output, and feedback matrices, we…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…
Specifications for reactive systems often consist of environment assumptions and system guarantees. An implementation should not only be correct, but also robust in the sense that it behaves reasonably even when the assumptions are…
Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…
Local reasoning about programs that combine aliasing and mutable state is a longstanding challenge. Existing approaches -- ownership systems, linear and affine types, uniqueness types, and lexical effect tracking -- impose global…
While LLMs have emerged as performant architectures for reasoning tasks, their compositional generalization capabilities have been questioned. In this work, we introduce a Compositional Generalization Challenge for Graph-based Commonsense…
This paper presents Grammar Reinforcement Learning (GRL), a reinforcement learning algorithm that uses Monte Carlo Tree Search (MCTS) and a transformer architecture that models a Pushdown Automaton (PDA) within a context-free grammar (CFG)…
User modeling aims to use language models (LMs) to mimic an individual's behavior from a corpus of past context-action pairs (e.g., conversation turns), enabling the simulation of users in settings like behavioral science, human-AI…
In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched systems satisfying Caratheodory…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
Proof schemata are a variant of LK-proofs able to simulate various induction schemes in first-order logic by adding so called proof links to the standard first-order LK-calculus. Proof links allow proofs to reference proofs thus giving…
The chase is a widely implemented approach to reason with tuple-generating dependencies (tgds), used in data exchange, data integration, and ontology-based query answering. However, it is merely a semi-decision procedure, which may fail to…