Related papers: Full Definability in a Profunctorial Model
Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Let $\cal R$ be an ordered vector space over an ordered division ring. We prove that every definable set $X$ is a finite union of relatively open definable subsets which are definably simply-connected, settling a conjecture from [5]. The…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
As machine learning algorithms getting adopted in an ever-increasing number of applications, interpretation has emerged as a crucial desideratum. In this paper, we propose a mathematical definition for the human-interpretable model. In…
Explainability has been widely stated as a cornerstone of the responsible and trustworthy use of machine learning models. With the ubiquitous use of Deep Neural Network (DNN) models expanding to risk-sensitive and safety-critical domains,…
Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
This paper examines how a notion of stable explanation developed elsewhere in Defeasible Logic can be expressed in the context of formal argumentation. With this done, we discuss the deontic meaning of this reconstruction and show how to…
We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…
We look at the proofs of a fragment of Linear Logic as a whole: in fact, Linear Logic's coherent semantics interprets the proofs of a given formula $A$ as faces of an abstract simplicial complex, thus allowing us to see the set of the…
The assertion that every definable set has a definable element is equivalent over ZF to the principle $V=\text{HOD}$, and indeed, we prove, so is the assertion merely that every $\Pi_2$-definable set has an ordinal-definable element.…
Faithful explanations are essential for machine learning models in high-stakes applications. Inherently interpretable models are well-suited for these applications because they naturally provide faithful explanations by revealing their…
The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domain-restricted but supports extensions including built-in functions as well…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We…
Motivated by a recent conjecture concerning the expressiveness of declarative networking, we propose a formal computation model for "eventually consistent" distributed querying, based on relational transducers. A tight link has been…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
We show that for every countable recursively saturated model $M$ of Peano Arithmetic and every subset $A \subseteq M$, there exists a full satisfaction class $S_A \subset M^2$ such that $A$ is definable in $(M,S_A)$ without parametres. It…