Related papers: Reasoning with Higher-Order Abstract Syntax in a L…

Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…

We describe a Martin-L\"of style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…

While Chain-of-Thought (CoT) prompting has significantly advanced the reasoning capabilities of Multimodal Large Language Models (MLLMs), relying solely on linear text sequences remains a bottleneck for complex tasks. We observe that even…

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…

Cedille is a relatively recent tool based on a Curry-style pure type theory, without a primitive datatype system. Using novel techniques based on dependent intersection types, inductive datatypes with their induction principles are derived.…

We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…

We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…

Intelligent coding systems are transforming software development by enabling users to specify code behavior in natural language. However, the opaque decision-making of AI-driven coders raises trust and usability concerns, particularly for…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…

We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…

We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due…

Large Language Models (LLMs) have shown remarkable reasoning ability through explicit Chain-of-Thought (CoT) prompting, but generating these step-by-step textual explanations is computationally expensive and slow. To overcome this, we aim…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…

Chain-of-Thought (CoT) reasoning successfully enhances the reasoning capabilities of Large Language Models (LLMs), yet it incurs substantial computational overhead for inference. Existing CoT compression methods often suffer from a critical…

Designing scalable concurrent objects, which can be efficiently used on multicore processors, often requires one to abandon standard specification techniques, such as linearizability, in favor of more relaxed consistency requirements.…

Chain-of-Thought (CoT) reasoning enhances large language models (LLMs) by decomposing complex problems into step-by-step solutions, improving performance on reasoning tasks. However, current CoT disclosure policies vary widely across…