Related papers: Logical Expressibility of Syntactic NL for Complem…
Neural language models (LMs) perform well on tasks that require sensitivity to syntactic structure. Drawing on the syntactic priming paradigm from psycholinguistics, we propose a novel technique to analyze the representations that enable…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
In this paper we develop a formal system called Natural Term Logic (NTL). NTL aims to represent key aspects of the logical and grammatical mechanisms of natural language as well as grammatical transformations which preserve core logical…
We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We establish fascinating…
We introduce SLR, an end-to-end framework for systematic evaluation and training of Large Language Models (LLMs) via Scalable Logical Reasoning. Given a user's task specification, SLR automatically synthesizes (i) an instruction prompt for…
Standpoint linear temporal logic ($SLTL$) is a recently introduced extension of classical linear temporal logic ($LTL$) with standpoint modalities. Intuitively, these modalities allow to express that, from agent $a$'s standpoint, it is…
Nominalistic Logic (NL) is a new presentation of Paul Gilmore's Intensional Type Theory (ITT) as a sequent calculus together with a succinct nominalization axiom (N) that permits names of predicates as individuals in certain cases. The…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…
We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be…
Recent large language models (LLMs) have achieved impressive reasoning milestones but continue to struggle with high computational costs, logical inconsistencies, and sharp performance degradation on high-complexity problems. While…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
This paper presents Non-Axiomatic Term Logic (NATL) as a theoretical computational framework of humanlike symbolic reasoning in artificial intelligence. NATL unites a discrete syntactic system inspired from Aristotle's term logic and a…
Propositional Linear Temporal Logic (LTL) is a popular formalism for specifying desirable requirements and security and privacy policies for software, networks, and systems. Yet expressing such requirements and policies in LTL remains…
Despite the recent progresses, particularly in developing Language Models, there are fundamental challenges and unanswered questions about how such models can continually learn/memorize, self-improve, and find effective solutions. In this…
Large language models have achieved substantial progress in mathematical reasoning, yet their advancement is limited by the scarcity of high-quality, high-difficulty training data. Existing synthesis methods largely rely on transforming…
Natural language is an intuitive way for humans to communicate tasks to a robot. While natural language (NL) is ambiguous, real world tasks and their safety requirements need to be communicated unambiguously. Signal Temporal Logic (STL) is…
In the field of Answer Set Programming (ASP), two logic programs are strongly equivalent if they are ordinarily equivalent under any extensions. This property provides a theoretical foundation for studying many aspects of logic programs…
Signal Temporal Logic (STL) is widely used to specify timed and safety-critical tasks for cyber-physical systems, but writing STL formulas directly is difficult for non-expert users. Natural language (NL) provides a convenient interface,…
We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…