Related papers: Kleene Algebra Modulo Theories
Weak Kleene logics are three-valued logics characterized by the presence of an infectious truth-value. In their external versions, as they were originally introduced by Bochvar and Hallden, these systems are equipped with an additional…
We show how concurrent quantales and concurrent Kleene algebras arise as convolution algebras $Q^X$ of functions from structures $X$ with two ternary relations that satisfy relational interchange laws into concurrent quantales or Kleene…
We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.
Multimodal latent reasoning has emerged as a promising paradigm that replaces explicit Chain-of-Thought (CoT) decoding with implicit feature propagation, simultaneously enhancing representation informativeness and reducing inference…
Repository-level code comprehension and knowledge sharing remain core challenges in software engineering. Large language models (LLMs) have shown promise by generating explanations of program structure and logic. However, these approaches…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
Reasoning models excel at complex tasks such as coding and mathematics, yet their inference is often slow and token-inefficient. To improve the inference efficiency, post-training quantization (PTQ) usually comes with the cost of large…
Generating proofs of unsatisfiability is a valuable capability of most SAT solvers, and is an active area of research for SMT solvers. This paper introduces the first method to efficiently generate proofs of unsatisfiability specifically…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
Restricted non-deterministic matrices (RNmatrices) impose constraints on the rows of non-deterministic matrices (Nmatrices), filtering out "unsound" rows and retaining only "valid" ones. This yields a more expressive framework than standard…
Knowledge tracing (KT) aims to predict students' responses to practices based on their historical question-answering behaviors. However, most current KT methods focus on improving overall AUC, leaving ample room for optimization in modeling…
We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…
Building on work of Maltsev on locally free algebras in finite purely functional languages, we revisit the model theory of (absolutely free) term algebras and their completions. Maltsev's analysis yields a natural axiomatization together…
A Kleene semiring is an algebraic structure satisfying the axioms of Kleene algebra, minus the annihilation axioms (x.0 = 0 = 0.x). We show that Kleene semirings (like Kleene algebras) admit the efficient elimination of various kinds of…
This survey reviews works in which language models (LMs) are augmented with reasoning skills and the ability to use tools. The former is defined as decomposing a potentially complex task into simpler subtasks while the latter consists in…
Foundational models with billions of parameters which have been trained on large corpora of data have demonstrated non-trivial skills in a variety of domains. However, due to their monolithic structure, it is challenging and expensive to…
Standard automated planning employs first-order formulas under closed-world semantics to achieve a goal with a given set of actions from an initial state. We follow a line of research that aims to incorporate background knowledge into…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
Recently, pre-trained language models like BERT have shown promising performance on multiple natural language processing tasks. However, the application of these models has been limited due to their huge size. To reduce its size, a popular…