We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the...
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Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However...
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Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only combine in trivial ways. This limits their usefulness in contexts where different intuitions are at play in different aspects of a problem. In particular, in some legal settings, different actors have different burdens of proof, which might be expressed as reasoning in different defeasible logics. In this paper, we introduce annotated defeasible logic as a flexible formalism permitting multiple forms of defeasibility, and establish some properties of the formalism.
Recent progress in logicprogramming (e.g., the development of the Answer Set programming paradigm) has made it possible to teach it to general undergraduate and even middle/high school students. Given the limited exp...
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logicprogramming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/ coinductive soundness of formulae is a challenging t...
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logicprogramming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/ coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logicprogramming for regular formulae. Another, less famous, but equally fundamental and important undecidable property is productivity. If a derivation is infinite and coinductively sound, we may ask whether the computed answer it determines actually computes an infinite formula. If it does, the infinite computation is productive. This intuition was first expressed under the name of computations at infinity in the 80s. In modern days of the Internet and stream processing, its importance lies in connection to infinite data structure processing. Recently, an algorithm was presented that semi-decides a weaker property -of productivity of logic programs. A logic program is productive if it can give rise to productive derivations. In this paper, we strengthen these recent results. We propose a method that semi-decides productivity of individual derivations for regular formulae. Thus, we at last give an algorithmic counterpart to the notion of productivity of derivations in logicprogramming. This is the first algorithmic solution to the problem since it was raised more than 30 years ago. We also present an implementation of this algorithm.
We argue that turning a logic program into a set of completed definitions can be sometimes thought of as the "reverse engineering" process of generating a set of conditions that could serve as a specificatio...
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We argue that turning a logic program into a set of completed definitions can be sometimes thought of as the "reverse engineering" process of generating a set of conditions that could serve as a specification for it. Accordingly, it may be useful to define completion for a large class of Answer Set programming (ASP) programs and to automate the process of generating and simplifying completion formulas. Examining the output produced by this kind of software may help programmers to see more clearly what their program does, and to what degree its behavior conforms with their expectations. As a step toward this goal, we propose here a definition of program completion for a large class of programs in the input language of the ASP grounder gringo, and study its properties.
The recent series 5 of the Answer Set programming (ASP) system clingo provides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constr...
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The recent series 5 of the Answer Set programming (ASP) system clingo provides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using these constraints in a reactive context. More precisely, we introduce extensions to clingo with difference and linear constraints over integers and reals, respectively, and realize them in complementary ways. Finally, we empirically evaluate the resulting clingo derivatives clingo[dl] and clingo[lp] on common language fragments and contrast them to related ASP systems.
One promising trend in digital system integration consists of boosting on-chip communication performance by means of silicon photonics, thus materializing the so-called Optical Networkson- Chip. Among them, wavelength...
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One promising trend in digital system integration consists of boosting on-chip communication performance by means of silicon photonics, thus materializing the so-called Optical Networkson- Chip. Among them, wavelength routing can be used to route a signal to destination by univocally associating a routing path to the wavelength of the optical carrier. Such wavelengths should be chosen so to minimize interferences among optical channels and to avoid routing faults. As a result, physical parameter selection of such networks requires the solution of complex constrained optimization problems. In previous work, published in the proceedings of the International Conference on Computer-Aided Design, we proposed and solved the problem of computing the maximum parallelism obtainable in the communication between any two endpoints while avoiding misrouting of optical signals. The underlying technology, only quickly mentioned in that paper, is Answer Set programming. In this work, we detail the Answer Set programming approach we used to solve such problem. Another important design issue is to select the wavelengths of optical carriers such that they are spread across the available spectrum, in order to reduce the likelihood that, due to imperfections in the manufacturing process, unintended routing faults arise. We show how to address such problem in Constraint logicprogramming on Finite Domains.
This paper describes an approach to the methodology of answer set programming that can facilitate the design of encodings that are easy to understand and provably correct. Under this approach, after appending a rule o...
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This paper describes an approach to the methodology of answer set programming that can facilitate the design of encodings that are easy to understand and provably correct. Under this approach, after appending a rule or a small group of rules to the emerging program, we include a comment that states what has been "achieved" so far. This strategy allows us to set out our understanding of the design of the program by describing the roles of small parts of the program in a mathematically precise way.
LPMLN is a recent addition to probabilistic logicprogramming languages. Its main idea is to overcome the rigid nature of the stable model semantics by assigning a weight to each rule in a way similar to Markov logic ...
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LPMLN is a recent addition to probabilistic logicprogramming languages. Its main idea is to overcome the rigid nature of the stable model semantics by assigning a weight to each rule in a way similar to Markov logic is defined. We present two implementations of LPMLN, LPMLN2ASP and LPMLN2MLN. System LPMLN2ASP translates LPMLN programs into the input language of answer set solver CLINGO, and using weak constraints and stable model enumeration, it can compute most probable stable models as well as exact conditional and marginal probabilities. System LPMLN2MLN translates LPMLN programs into the input language of Markov logic solvers, such as alchemy, TUFFY, and ROCKIT, and allows for performing approximate probabilistic inference on LPMLN programs. We also demonstrate the usefulness of the LPMLN systems for computing other languages, such as ProbLog and Pearl's Causal Models, that are shown to be translatable into LPMLN.
In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to corresp...
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In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of learning default theories. Default logic is what humans employ in common-sense reasoning. Therefore, learned default theories are better understood by humans. In this paper, we present new algorithms to learn default theories in the form of non-monotonic logic programs. Experiments reported in this paper show that our algorithms are a significant improvement over traditional approaches based on inductive logicprogramming. Under consideration for acceptance in TPLP.
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