Related papers: Integrating Logic Rules with Everything Else, Seam…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
Formal, mathematically rigorous programming language semantics are the essential prerequisite for the design of logics and calculi that permit automated reasoning about concurrent programs. We propose a novel modular semantics designed to…
Vision-Language-Action (VLA) models mark a transformative advancement in artificial intelligence, aiming to unify perception, natural language understanding, and embodied action within a single computational framework. This foundational…
Autonomous driving systems face significant challenges in achieving human-like adaptability, robustness, and interpretability in complex, open-world environments. These challenges stem from fragmented architectures, limited generalization…
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…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
Intuitionistic logic programming provides the notion of embedded implication in rule bodies, which can be used to reason about a current database modified by the antecedent. This can be applied to a system that translates SQL to Datalog to…
Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows for expressing every property of finite structures that is decidable in the complexity class SigmaP2 (= NP^NP). Despite this high expressiveness, there are some…
We present a computable algorithm that assigns probabilities to every logical statement in a given formal language, and refines those probabilities over time. For instance, if the language is Peano arithmetic, it assigns probabilities to…
We introduce a new programming language construct, Interactors, supporting the agent-oriented view that programming is a dialog between simple, self-contained, autonomous building blocks. We define Interactors as an abstraction of answer…
Integrating architectural elements with a modern programming language is essential to ensure a smooth combination of architectural design and programming. In this position statement, we motivate a combination of architectural description…
We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence…
This paper introduces SOLID (Synergizing Optimization and Large Language Models for Intelligent Decision-Making), a novel framework that integrates mathematical optimization with the contextual capabilities of large language models (LLMs).…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…
Transforming fragmented enterprise data into actionable insights remains a significant challenge for LLMs, constrained by complex database schemas, limitations in dynamic SQL generation, and the need for deep multi-dimensional analysis.In…
Adapting driving behavior to new environments, customs, and laws is a long-standing problem in autonomous driving, precluding the widespread deployment of autonomous vehicles (AVs). In this paper, we present LLaDA, a simple yet powerful…
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…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…