Related papers: PDDL Axioms Are Equivalent to Least Fixed Point Lo…
Large Language Models have been found to create plans that are neither executable nor verifiable in grounded environments. An emerging line of work demonstrates success in using the LLM as a formalizer to generate a formal representation of…
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 symbolic planning systems, the knowledge on the domain is commonly provided by an expert. Recently, an automatic abstraction procedure has been proposed in the literature to create a Planning Domain Definition Language (PDDL)…
Representation of defeasible information is of interest in description logics, as it is related to the need of accommodating exceptional instances in knowledge bases. In this direction, in our previous works we presented a datalog…
The Planning Domain Definition Language (PDDL) is the state-of-the-art language for specifying planning problems in artificial intelligence research. Writing and maintaining these planning problems, however, can be time-consuming and error…
Most approaches for repairing description logic (DL) ontologies aim at changing the axioms as little as possible while solving inconsistencies, incoherences and other types of undesired behaviours. As in Belief Change, these issues are…
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…
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular…
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…
Generating an abstraction of a dynamic domain that aligns with a given purpose remains a significant challenge given that the choice of such an abstraction can impact an agent's ability to plan, reason, and provide explanations effectively.…
There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing…
Several solutions for specifying normative artefacts (norms, contracts, policies) in a computational processable way have been presented in the literature. Legal core ontologies have been proposed to systematize concepts and relationships…
Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic…
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…
We introduce $\mathcal{DLR}^+$, an extension of the n-ary propositionally closed description logic $\mathcal{DLR}$ to deal with attribute-labelled tuples (generalising the positional notation), projections of relations, and global and local…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
We present Probabilistic Decision Model and Notation (pDMN), a probabilistic extension of Decision Model and Notation (DMN). DMN is a modeling notation for deterministic decision logic, which intends to be user-friendly and low in…
Datalog is a lightweight logic programming language, based on the logic of Horn clauses. Lean, on the other hand, is a proof assistant system and language based on the Calculus of Inductive Constructions (CIC). Datalog is more constrained…
Classical planning formulations like the Planning Domain Definition Language (PDDL) admit action sequences guaranteed to achieve a goal state given an initial state if any are possible. However, reasoning problems defined in PDDL do not…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…