Related papers: Defeasible Reasoning via Datalog$^\neg$
Defeasible statements are statements that are likely, or probable, or usually true, but may occasionally be false. Plausible reasoning makes conclusions from statements that are either facts or defeasible statements without using numbers.…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
Datalog$^\neg$ is a central formalism used in a variety of domains ranging from deductive databases and abstract argumentation frameworks to answer set programming. Its model theory is the finite counterpart of the logical semantics…
We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the…
Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…
In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data…
We analyse so-called computable laws, i.e., laws that can be enforced by automatic procedures. These laws should be logically perfect and unambiguous, but sometimes they are not. We use a regulation on road transport to illustrate this…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
We present realizability and realization logic, two program logics that jointly address the problem of finding solutions in semantics-guided synthesis. What is new is that we proceed eagerly and not only analyze a single candidate program…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
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…
Termination of logic programs with negated body atoms (here called general logic programs) is an important topic. One reason is that many computational mechanisms used to process negated atoms, like Clark's negation as failure and Chan's…
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
This paper describes a resolution based Description Logic reasoning system called DLog. DLog transforms Description Logic axioms into a Prolog program and uses the standard Prolog execution for efficiently answering instance retrieval…
$\{log\}$ 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.…
Advances in logic programming and increasing industrial uptake of Datalog-inspired approaches demonstrate the emerging need to express powerful code analyses more easily. Declarative program analysis frameworks (e.g., using logic…