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We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible…
Block-encodings are ubiquitous in quantum computing as a way to represent data within a unitary operator. While several unstructured methods are applicable to arbitrary data, these techniques are burdened by hidden costs and poor accuracy.…
Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…
A core problem in learning semantic parsers from denotations is picking out consistent logical forms--those that yield the correct denotation--from a combinatorially large space. To control the search space, previous work relied on…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
A recent strand of research in structural proof theory aims at exploring the notion of analytic calculi (i.e. those calculi that support general and modular proof-strategies for cut elimination), and at identifying classes of logics that…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
Ontologies and knowledge graphs require continuous evolution to remain comprehensive and accurate, but manual curation is labor intensive. Large Language Models (LLMs) possess vast unstructured knowledge but struggle with maintaining…
We develop a system for solving logical deduction one-dimensional ordering problems by transforming natural language premises and candidate statements into first-order logic. Building on Heim and Kratzer's syntax-based compositional…
Logic locking as a solution for semiconductor intellectual property (IP) confidentiality has received considerable attention in academia, but has yet to produce a viable solution to protect against known threats. In part due to a lack of…
As one of their many applications, large language models (LLMs) have recently shown promise in automating register transfer level (RTL) code generation. However, conventional LLM decoding strategies, originally designed for natural…
In the rewriting logic framework, equational-based specifications are used to define deterministic functional behavior, abstract data types, and canonical representations of data. These specifications include a (possibly order-sorted)…
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…
Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain…
While large language models (LLMs) have demonstrated remarkable reasoning capabilities, they often struggle with complex tasks that require specific thinking paradigms, such as divide-and-conquer and procedural deduction, \etc Previous…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…