Related papers: Fixpoint Semantics for DatalogMTL with Negation
DatalogMTL is a powerful rule-based language for temporal reasoning. Due to its high expressive power and flexible modeling capabilities, it is suitable for a wide range of applications, including tasks from industrial and financial…
Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…
The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
Recently, a novel fixed point operation has been introduced over certain non-monotonic functions between stratified complete lattices and used to give semantics to logic programs with negation and boolean context-free grammars. We prove…
We compare the conceptual strength of two axiomatic theories of truth: KF and WKF. The first one has been designed to capture Kripke's fixed-point construction based on Strong Kleene logic. The second one is based on the Weak Kleene…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented…
Alternating-time temporal logic (ATL) allows to specify requirements on abilities that different agents should (or should not) possess in a multi-agent system. However, model checking ATL specifications in realistic systems is…
Linear temporal logic (LTL) is used in system verification to write formal specifications for reactive systems. However, some relevant properties, e.g. non-inference in information flow security, cannot be expressed in LTL. A class of such…
We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the…
Hybrid Knowledge Bases based on Lifschitz's logic of Minimal Knowledge with Negation as Failure are a successful approach to combine the expressivity of Description Logics and Logic Programming in a single language. Their syntax, defined by…
This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator…
In this work, we measure the impact of affixal negation on modern English large language models (LLMs). In affixal negation, the negated meaning is expressed through a negative morpheme, which is potentially challenging for LLMs as their…
Satisfiability modulo theories (SMT) solving has become a critical part of many static analyses, including symbolic execution, refinement type checking, and model checking. We propose Formulog, a domain-specific language that makes it…
In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog that consists of the language LO enriched with the constant 1. We use constraints…
This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point…