Attributional inference, the ability to predict latent intentions behind observed actions, is a critical yet underexplored capability for large language models (LLMs) operating in multi-agent environments. Traditional natural language inference (NLI), in fact, fails to capture the nuanced, intention-driven reasoning essential for complex interactive systems. To address this gap, we introduce Attributional NLI (Att-NLI), a framework that extends NLI with principles from social psychology to assess an agent's capacity for abductive intentional inference (generating hypotheses about latent intentions), and subsequent deductive verification (drawing valid logical conclusions). We instantiate Att-NLI via a textual game, Undercover-V, experimenting with three types of LLM agents with varying reasoning capabilities and access to external tools: a standard NLI agent using only deductive inference, an Att-NLI agent employing abductive-deductive inference, and a neuro-symbolic Att-NLI agent performing abductive-deductive inference with external theorem provers. Extensive experiments demonstrate a clear hierarchy of attributional inference capabilities, with neuro-symbolic agents consistently outperforming others, achieving an average win rate of 17.08%. Our results underscore the role that Att-NLI can play in developing agents with sophisticated reasoning capabilities, highlighting, at the same time, the potential impact of neuro-symbolic AI in building rational LLM agents acting in multi-agent environments.