Related papers: $\omega$PAP Spaces: Reasoning Denotationally About…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…
Cai and Hemachandra used iterative constant-setting to prove that Few $\subseteq$ $\oplus$P (and thus that FewP $\subseteq$ $\oplus$P). In this paper, we note that there is a tension between the nondeterministic ambiguity of the class one…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
This article develops a novel operational semantics for probabilistic control-flow graphs (pCFGs) of probabilistic imperative programs with random assignment and "observe" (or conditioning) statements. The semantics transforms probability…
The paper is devoted to showing how to systematically design a programming language in 'reverse order', i.e. from denotations to syntax. This construction is developed in an algebraic framework consisting of three many-sorted algebras: of…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
A new theory of programming is proposed. The theory consists of OE (Operation Expression), SP (Semantic Predicate) and A (Axiom), abbreviated as OESPA. OE is for programming: its syntax is given by BNF formulas and its semantics is defined…
Many segmentation tasks, such as medical image segmentation or future state prediction, are inherently ambiguous, meaning that multiple predictions are equally correct. Current methods typically rely on generative models to capture this…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…
We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving…
We present a simple functional programming language, called Dual PCF, that implements forward mode automatic differentiation using dual numbers in the framework of exact real number computation. The main new feature of this language is the…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
Prediction sets have recently been shown to be a promising strategy for quantifying the uncertainty of deep neural networks in a way that provides theoretical guarantees. However, existing techniques have largely targeted settings where the…
G\"odel's Dialectica has been introduced and developed in the tradition of the so-called functional interpretations. Only recently has it been related with the a priori unrelated notion of differentiation, by taking a program-theoretic…
Probabilistic programming has become a standard practice to model stochastic events and learn about the behavior of nature in different scientific contexts, ranging from Genetics and Ecology to Linguistics and Psychology. However, domain…
In this work, we study the fully automated inference of expected result values of probabilistic programs in the presence of natural programming constructs such as procedures, local variables and recursion. While crucial, capturing these…