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Efficient power production scheduling is a crucial concern for power system operators aiming to minimize operational costs. Previous mixed-integer linear programming formulations for unit commitment (UC) problems have primarily used two or…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
Continual learning of new knowledge over time is one desirable capability for intelligent systems to recognize more and more classes of objects. Without or with very limited amount of old data stored, an intelligent system often…
Reasoning large language models achieve impressive test-time scaling by thinking for longer, but this performance gain comes at significant compute cost. Directly limiting test-time budget hurts overall performance, but not all problems are…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…
Coherence is a crucial aspect of evaluating text readability and can be assessed through two primary factors when evaluating an essay in a scoring scenario. The first factor is logical coherence, characterized by the appropriate use of…
Forgetting is in common in daily life, and 50-80% everyday's forgetting is due to prospective memory failures, which have significant impacts on our life. More seriously, some of these memory lapses can bring fatal consequences such as…
Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higher-order moments are poorly understood. The existing formulas are either not general enough, or not structured and…
A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or…
We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms.…
We design learning algorithms for synthesizing invariants using Horn implication counterexamples (Horn-ICE), extending the ICE-learning model. In particular, we describe a decision-tree learning algorithm that learns from Horn-ICE samples,…
In this paper we study the expressive power of Horn-formulae in dependence logic and show that they can express NP-complete problems. Therefore we define an even smaller fragment D-Horn* and show that over finite successor structures it…
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…
Most existing approaches to hashing apply a single form of hash function, and an optimization process which is typically deeply coupled to this specific form. This tight coupling restricts the flexibility of the method to respond to the…
Dictionary learning aims at seeking a dictionary under which the training data can be sparsely represented. Methods in the literature typically formulate the dictionary learning problem as an optimization w.r.t. two variables, i.e.,…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…
While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…