Related papers: Predicate Transformers and Linear Logic, yet anoth…
Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…
Transformers have the capacity to act as supervised learning algorithms: by properly encoding a set of labeled training ("in-context") examples and an unlabeled test example into an input sequence of vectors of the same dimension, the…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…
Discrete-choice models, such as Multinomial Logit, Probit, or Mixed-Logit, are widely used in Marketing, Economics, and Operations Research: given a set of alternatives, the customer is modeled as choosing one of the alternatives to…
We study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
Deontic logics are formalisms for reasoning over norms, obligations, permissions and prohibitions. Input/Output (I/O) Logics are a particular family of so-called norm-based deontic logics that formalize conditional norms outside of the…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
Refinement types -- types qualified with logical predicates -- have proven effective for lightweight verification in languages like Liquid Haskell, F*, and Dafny. However, in these systems refinements are either written in a separate…
The work relates to the automatic generation of logical specifications, considered as sets of temporal logic formulas, extracted directly from developed software models. The extraction process is based on the assumption that the whole…
Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as…
Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
This paper describes a semantics for pure Prolog programs with negation that provides meaning to metaprograms. Metaprograms are programs that construct and use data structures as programs. In Prolog a primary mataprogramming construct is…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…