Logic programs with ordered disjunction: First-order semantics and expressiveness

Logic programs with ordered disjunction (LPODs) (Brewka 2002) generalize normal logic programs by combining alternative and ranked options in the heads of rules. It has been showed that LPODs are useful in a number of areas including game theory, policy languages, planning and argumentations. In this paper, we extend propositional LPODs to the first-order case, where a classical second-order formula is defined to capture the stable model semantics of the underlying first-order LPODs. We then develop a progression semantics that is equivalent to the stable model semantics but naturally represents the reasoning procedure of LPODs. We show that on finite structures, every LPOD can be translated to a firstorder sentence, which provides a basis for computing stable models of LPODs. We further study the complexity and expressiveness of LPODs and prove that almost positive LPODs precisely capture first-order normal logic programs, which indicates that ordered disjunction itself and constraints are sufficient to represent negation as failure.NPRP grant (NPRP 09-079-1-013) from the Qatar National Research Fund (QNRF).Scopu

Automatic Music Composition using Answer Set Programming

Music composition used to be a pen and paper activity. These these days music is often composed with the aid of computer software, even to the point where the computer compose parts of the score autonomously. The composition of most styles of music is governed by rules. We show that by approaching the automation, analysis and verification of composition as a knowledge representation task and formalising these rules in a suitable logical language, powerful and expressive intelligent composition tools can be easily built. This application paper describes the use of answer set programming to construct an automated system, named ANTON, that can compose melodic, harmonic and rhythmic music, diagnose errors in human compositions and serve as a computer-aided composition tool. The combination of harmonic, rhythmic and melodic composition in a single framework makes ANTON unique in the growing area of algorithmic composition. With near real-time composition, ANTON reaches the point where it can not only be used as a component in an interactive composition tool but also has the potential for live performances and concerts or automatically generated background music in a variety of applications. With the use of a fully declarative language and an "off-the-shelf" reasoning engine, ANTON provides the human composer a tool which is significantly simpler, more compact and more versatile than other existing systems. This paper has been accepted for publication in Theory and Practice of Logic Programming (TPLP).Comment: 31 pages, 10 figures. Extended version of our ICLP2008 paper. Formatted following TPLP guideline

Progression and Verification of Situation Calculus Agents with Bounded Beliefs

We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories. © 2015 The Author(s

LTLf/LDLf Non-Markovian Rewards

In Markov Decision Processes (MDPs), the reward obtained in a state is Markovian, i.e., depends on the last state and action. This dependency makes it difficult to reward more interesting long-term behaviors, such as always closing a door after it has been opened, or providing coffee only following a request. Extending MDPs to handle non-Markovian reward functions was the subject of two previous lines of work. Both use LTL variants to specify the reward function and then compile the new model back into a Markovian model. Building on recent progress in temporal logics over finite traces, we adopt LDLf for specifying non-Markovian rewards and provide an elegant automata construction for building a Markovian model, which extends that of previous work and offers strong minimality and compositionality guarantees

Polynomial Size Analysis of First-Order Shapely Functions

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be implementations of matrix multiplication and the Cartesian product of two lists. The type system is proved to be sound w.r.t. the operational semantics of the language. The type checking problem is shown to be undecidable in general. We define a natural syntactic restriction such that the type checking becomes decidable, even though size polynomials are not necessarily linear or monotonic. Furthermore, we have shown that the type-inference problem is at least semi-decidable (under this restriction). We have implemented a procedure that combines run-time testing and type-checking to automatically obtain size dependencies. It terminates on total typable function definitions.Comment: 35 pages, 1 figur

Reasoning about goal-directed real-time teleo-reactive programs

The teleo-reactive programming model is a high-level approach to developing real-time systems that supports hierarchical composition and durative actions. The model is different from frameworks such as action systems, timed automata and TLA+, and allows programs to be more compact and descriptive of their intended behaviour. Teleo-reactive programs are particularly useful for implementing controllers for autonomous agents that must react robustly to their dynamically changing environments. In this paper, we develop a real-time logic that is based on Duration Calculus and use this logic to formalise the semantics of teleo-reactive programs. We develop rely/guarantee rules that facilitate reasoning about a program and its environment in a compositional manner. We present several theorems for simplifying proofs of teleo-reactive programs and present a partially mechanised method for proving progress properties of goal-directed agents. © 2013 British Computer Society

Towards Ideal Semantics for Analyzing Stream Reasoning

The rise of smart applications has drawn interest to logical reasoning over data streams. Recently, different query languages and stream processing/reasoning engines were proposed in different communities. However, due to a lack of theoretical foundations, the expressivity and semantics of these diverse approaches are given only informally. Towards clear specifications and means for analytic study, a formal framework is needed to define their semantics in precise terms. To this end, we present a first step towards an ideal semantics that allows for exact descriptions and comparisons of stream reasoning systems.Comment: International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), co-located with the 21st European Conference on Artificial Intelligence (ECAI 2014). Proceedings of the International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), pages 17-22, technical report, ISSN 1430-3701, Leipzig University, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-150562 2014,