Related papers: A decidable subclass of finitary programs
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according…
Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
We take up an idea from the folklore of Answer Set Programming, namely that choices, integrity constraints along with a restricted rule format is sufficient for Answer Set Programming. We elaborate upon the foundations of this idea in the…
We present a logical system CFP (Concurrent Fixed Point Logic) supporting the extraction of nondeterministic and concurrent programs that are provably total and correct. CFP is an intuitionistic first-order logic with inductive and…
The possibility of translating logic programs into functional ones has long been a subject of investigation. Common to the many approaches is that the original logic program, in order to be translated, needs to be well-moded and this has…
The relevance of machine learning (ML) in our daily lives is closely intertwined with its explainability. Explainability can allow end-users to have a transparent and humane reckoning of a ML scheme's capability and utility. It will also…
Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka et al. KR 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…
Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which…
The paper presents two equivalent definitions of answer sets for logic programs with aggregates. These definitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice.…
Function calling empowers large language models (LLMs) to interface with external tools, yet existing RL-based approaches suffer from misalignment between reasoning processes and tool-call decisions. We propose R2IF, a reasoning-aware RL…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds,…
Declarative styles such as functional programming (FP) are rapidly gaining ground on their imperative cousins, including procedural and object-oriented programming. The shift is subtle because it is happening within the context of…
Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic functions. Two semantic alternatives have been usually considered for…