Pearl observes that causal knowledge enables predicting the effects of interventions, such as actions, whereas descriptive knowledge only permits drawing conclusions from observation. This paper extends Pearl's approach to causality and interventions to the setting of stratified abductive logic programs. It shows how stable models of such programs can be given a causal interpretation by building on philosophical foundations and recent work by Bochman and Eelink et al. In particular, it provides a translation of abductive logic programs into causal systems, thereby clarifying the informal causal reading of logic program rules and supporting principled reasoning about external actions. The main result establishes that the stable model semantics for stratified programs conforms to key philosophical principles of causation, such as causal sufficiency, natural necessity, and irrelevance of unobserved effects. This justifies the use of stratified abductive logic programs as a framework for causal modeling and for predicting the effects of interventions.

Answer Set Programming Modulo Theories (ASPMT) is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a recent proposal of the functional stable model semantics by fixing interpretations of background theories. Analogously to a known relationship between ASP and SA T, "tight" ASPMT programs can be translated into SMT instances. We demonstrate the usefulness of ASPMT by enhancing action language C + to handle continuous changes as well as discrete changes. We reformulate the semantics of C + in terms of ASPMT, and show that SMT solvers can be used to compute the language. We also show how the language can represent cumulative effects on continuous resources.

Action languages are formal models of parts of natural language that are designed to describe effects of actions. Many of these languages can be viewed as high level notations of answer set programs structured to represent transition systems. However, the form of answer set programs considered in the earlier work is quite limited in comparison with the modern Answer Set Programming (ASP) language, which allows several useful constructs for knowledge representation, such as choice rules, aggregates, and abstract constraint atoms. We propose a new action language called BC+, which closes the gap between action languages and the modern ASP language. The main idea is to define the semantics of BC+ in terms of general stable model semantics for propositional formulas, under which many modern ASP language constructs can be identified with shorthands for propositional formulas. Language BC+ turns out to be sufficiently expressive to encompass the best features of other action languages, such as languages B, C, C+, and BC. Computational methods available in ASP solvers are readily applicable to compute BC+, which led to an implementation of the language by extending system cplus2asp.

LPMLN is a recently introduced formalism that extends answer set programs by adopting the log-linear weight scheme of Markov Logic. This paper investigates the relationships between LPMLN and two other extensions of answer set programs: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. We present a translation of LPMLN into programs with weak constraints and a translation of P-log into LPMLN, which complement the existing translations in the opposite directions. The first translation allows us to compute the most probable stable models (i.e., MAP estimates) of LPMLN programs using standard ASP solvers. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl's Causal Models, that are shown to be translatable into LPMLN. The second translation tells us how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers and MLN solvers.

We define a stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. The syntax of the language is the same as the syntax of fuzzy propositional logic, but its semantics distinguishes stable models from non-stable models. The generality of the language allows for highly configurable nonmonotonic reasoning for dynamic domains involving graded truth degrees. We show that several properties of Boolean stable models are naturally extended to this many-valued setting, and discuss how it is related to other approaches to combining fuzzy logic and the stable model semantics.

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 developed for normal logic programs, mainly based on the notions of Clark's completion and two-valued or three-valued canonical models including supported, stable, regular and well-founded models. In this paper we establish a formal link between Datalog$^\neg$ and Boolean network theory first introduced for gene regulatory networks. We show that in the absence of odd cycles in a Datalog$^\neg$ program, the regular models coincide with the stable models, which entails the existence of stable models, and in the absence of even cycles, we prove the uniqueness of stable partial models and regular models. This connection also gives new upper bounds on the numbers of stable partial, regular, and stable models of a Datalog$^\neg$ program using the cardinality of a feedback vertex set in its atom dependency graph. Interestingly, our connection to Boolean network theory also points us to the notion of trap spaces. In particular we show the equivalence between subset-minimal stable trap spaces and regular models.

Answer-set programming (ASP) is a successful problem-solving approach in logic-based AI. In ASP, problems are represented as declarative logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, based on a monotonic logic called here-and-there logic. EL was basically proposed by Pearce as a foundational framework of ASP. Epistemic specifications (ES) are extensions of ASP-programs with subjective literals. These new modal constructs in the ASP-language make it possible to check whether a regular literal of ASP is true in every (or some) answer-set of a program. ES-programs are interpreted by world-views, which are essentially collections of answer-sets. (Reflexive) autoepistemic logic is a nonmonotonic formalism, modeling self-belief (knowledge) of ideally rational agents. A relatively new semantics for ES is based on a combination of EL and (reflexive) autoepistemic logic. In this paper, we first propose an overarching framework in the epistemic ASP domain. We then establish a correspondence between existing (reflexive) (auto)epistemic equilibrium logics and our easily-adaptable comprehensive framework, building on Pearce's characterisation of answer-sets as equilibrium models. We achieve this by extending Ferraris' work on answer sets for propositional theories to the epistemic case and reveal the relationship between some ES-semantic proposals.

The growing popularity of Answer Set Programming (ASP; [13]) in both academia and industry necessitates the development of user-friendly graphical interfaces to cater to end users. This is especially critical for interactive applications where users engage in iterative feedback loops with ASP systems. Examples include timetabling or product configuration tools. This leads to challenges in frontend development and requires skills in areas beyond ASP development. In addition, custom solutions have a limited reach, as they cannot be easily adapted. Clinguin addresses this challenge and streamlines User Interface (UI) development for ASP developers by letting them build interactive prototypes directly in ASP, eliminating the need for separate frontend languages. To this end, clinguin uses a few dedicated predicates to define UIs and the treatment of user-triggered events.

We investigates the concept of strong equivalence within the extended framework of Answer Set Programming with constraints. Two groups of rules are considered strongly equivalent if, informally speaking, they have the same meaning in any context. We demonstrate that, under certain assumptions, strong equivalence between rule sets in this extended setting can be precisely characterized by their equivalence in the logic of Here-and-There with constraints. Furthermore, we present a translation from the language of several clingo-based answer set solvers that handle constraints into the language of Here-and-There with constraints. This translation enables us to leverage the logic of Here-and-There to reason about strong equivalence within the context of these solvers. We also explore the computational complexity of determining strong equivalence in this context.

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we propose Answer Set Networks (ASN), a NeSy solver. Based on Graph Neural Networks (GNN), ASNs are a scalable approach to ASP-based Deep Probabilistic Logic Programming (DPPL). Specifically, we show how to translate ASPs into ASNs and demonstrate how ASNs can efficiently solve the encoded problem by leveraging GPU's batching and parallelization capabilities. Our experimental evaluations demonstrate that ASNs outperform state-of-the-art CPU-bound NeSy systems on multiple tasks. Simultaneously, we make the following two contributions based on the strengths of ASNs. Namely, we are the first to show the finetuning of Large Language Models (LLM) with DPPLs, employing ASNs to guide the training with logic. Further, we show the "constitutional navigation" of drones, i.e., encoding public aviation laws in an ASN for routing Unmanned Aerial Vehicles in uncertain environments.