Related papers: Integration in Cones
In \cite{sp25}, continuous information frames were introduced that capture exactly all continuous domains. They are obtained from the information frames considered in \cite{sp21} by omitting the conservativity requirement. Information…
Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible…
Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…
The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by…
Sofic and hyperlinear groups are the countable discrete groups that can be approximated in a suitable sense by finite symmetric groups and groups of unitary matrices. These notions turned out to be very deep and fruitful, and stimulated in…
We propose a method to adapt functional logic programming to deal with reasoning on coinductively interpreted programs as well as on inductively interpreted programs. In order to do so, we consider a class of objects interesting for this…
Large Language Models (LLMs) are becoming increasingly popular in pervasive computing due to their versatility and strong performance. However, despite their ubiquitous use, the exact mechanisms underlying their outstanding performance…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
With the recent success of embeddings in natural language processing, research has been conducted into applying similar methods to code analysis. Most works attempt to process the code directly or use a syntactic tree representation,…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
A polymorphic analysis is an analysis whose input and output contain parameters which serve as placeholders for information that is unknown before analysis but provided after analysis. In this paper, we present a polymorphic groundness…
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,…
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
We consider a problem of data integration. Consider determining which genes affect a disease. The genes, which we call predictor objects, can be measured in different experiments on the same individual. We address the question of finding…
Applicative functors are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell. Applicative functors are to be preferred to monads when the structure of a computation…
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…