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We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…
NLP tasks differ in the semantic information they require, and at this time no single se- mantic representation fulfills all requirements. Logic-based representations characterize sentence structure, but do not capture the graded aspect of…
We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics,…
Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning…
We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branching. We give its operational semantics in terms of special…
Semantic communication has emerged as a promising paradigm to address the challenges of next-generation communication networks. While some progress has been made in its conceptualization, fundamental questions remain unresolved. In this…
We develop a denotational model for probabilistic and concurrent imperative programs, a class of programs with standard control flow via conditionals and while-loops, as well as probabilistic actions and parallel composition. Whereas…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks…
We present a new symbolic execution semantics of probabilistic programs that include observe statements and sampling from continuous distributions. Building on Kozen's seminal work, this symbolic semantics consists of a countable collection…
Distributional semantics creates vector-space representations that capture many forms of semantic similarity, but their relation to semantic entailment has been less clear. We propose a vector-space model which provides a formal foundation…
The Semantic Web effort has steadily been gaining traction in the recent years. In particular,Web search companies are recently realizing that their products need to evolve towards having richer semantic search capabilities. Description…
The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension…
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
Both syntactic and semantic structures are key linguistic contextual clues, in which parsing the latter has been well shown beneficial from parsing the former. However, few works ever made an attempt to let semantic parsing help syntactic…
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…
Programmability and verifiability lie at the heart of the software-defined networking paradigm. While OpenFlow and its match-action concept provide primitive operations to manipulate hardware configurations, over the last years, several…
Semantic parsers convert natural language to logical forms, which can be evaluated on knowledge bases (KBs) to produce denotations. Recent semantic parsers have been developed with sequence-to-sequence (seq2seq) pre-trained language models…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability…