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In recent years, the effort to formalize erotetic inferences---i.e., inferences to and from questions---has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these…
Despite their impressive capabilities, large pre-trained language models (LMs) struggle with consistent reasoning; recently, prompting LMs to generate explanations that self-guide the inference has emerged as a promising direction to amend…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
\ac{CoT} prompting improves LLM accuracy on complex tasks but often increases token usage and inference cost. Existing ``Budget Forcing'' methods reduce cost via fine-tuning with heuristic length penalties, suppressing both essential…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
I shall argue that a resolution of the PvNP problem requires building an iff bridge between the domain of provability and that of computability. The former concerns how a human intelligence decides the truth of number-theoretic relations,…
We define a class of formal systems inspired by Prawitz's theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to…
Our main result (Theorem A) shows the incompleteness of any consistent sequential theory T formulated in a finite language such that T is axiomatized by a collection of sentences of bounded quantifier-alternation-depth. Our proof employs an…
Inductive Logic Programming (ILP) provides interpretable rule learning in relational domains, yet remains limited in its ability to induce and reason with numerical constraints. Classical ILP systems operate over discrete predicates and…
Temporal stream logic (TSL) extends LTL with updates and predicates over arbitrary function terms. This allows for specifying data-intensive systems for which LTL is not expressive enough. In the semantics of TSL, functions and predicates…
The Ideal Proof System (IPS) of Grochow & Pitassi (FOCS 2014, J. ACM, 2018) is an algebraic proof system that uses algebraic circuits to refute the solvability of unsatisfiable systems of polynomial equations. One potential drawback of IPS…
Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems using pretrained large language models (LLMs). In this work, we analyze CoT prompting from a statistical…
Prosody is essential for speech technology, shaping comprehension, naturalness, and expressiveness. However, current text-to-speech (TTS) systems still struggle to accurately capture human-like prosodic variation, in part because existing…
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal…
Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…
The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logico-algebraic objects. As a result, the logic of experimental…
The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…
Unbounded {\L}ukasiewicz logic is a substructural logic that combines features of infinite-valued {\L}ukasiewicz logic with those of abelian logic. The logic is finitely strongly complete w.r.t.~the additive $\ell$-group on the reals…
Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the…