We propose a method for computing supported models of normal logic programs in vector spaces using gradient information. First, the program is translated into a definite program and embedded into a matrix representing...
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ISBN:
(纸本)9783031157073;9783031157066
We propose a method for computing supported models of normal logic programs in vector spaces using gradient information. First, the program is translated into a definite program and embedded into a matrix representing the program. We introduce a loss function based on the implementation of the immediate consequence operator T-P by matrix-vector multiplication with a suitable thresholding function, and we incorporate regularization terms into the loss function to avoid undesirable results. the proposed thresholding operation is an almost everywhere differentiable alternative to the non-linear thresholding operation. We report the results of several experiments where our method shows promising performance when used with adaptive gradient update.
Modal logic S5 is used extensively for representing knowledge that includes statements about necessity and possibility, owing to its simplicity in handling chained modal operators. Significant research effort has been...
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ISBN:
(纸本)9783031157073;9783031157066
Modal logic S5 is used extensively for representing knowledge that includes statements about necessity and possibility, owing to its simplicity in handling chained modal operators. Significant research effort has been devoted in developing efficient reasoning mechanisms over complex S5 formulas, resulting in various solvers taking advantage of the boolean satisfiability problem (SAT). Among them, the most performant solver implements a heuristic for identifying worlds that can be merged, hence reducing the size of SAT instances to be checked. Recently, Answer Set programming (ASP) has also been considered, and different ASP encodings were proposed and tested, reaching state-of-the-art performance. In particular, a heuristic for identifying the propositional atoms that are relevant in every world resulted in a performance gain in previous experiments. this work addresses the open question of whether the aforementioned two heuristics can be combined, as well as possibly enabling lazy instantiation of the resulting encodings, and what their potential impact is on the performance of the ASP-based solver. Experiments show that lazy creation of worlds provides some further performance gain to the ASP-based solver on the tested instances.
Model-based Diagnosis (MBD) is an approach to diagnosis, where an (objective) model of a system is diagnosed to find a set of explanations revealing root causes for issues. Temporal behavioral models are prominent app...
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ISBN:
(纸本)9783031157073;9783031157066
Model-based Diagnosis (MBD) is an approach to diagnosis, where an (objective) model of a system is diagnosed to find a set of explanations revealing root causes for issues. Temporal behavioral models are prominent approach for temporal MBD, where their associated temporal formulas (TBFs) by Brusoni et al. (Artificial Intelligence, 102:39-79, 1998) can be used to relate explanations to observations under temporal constraints based on Allen's Interval Algebra (IA). Due to expressive limitations of the constructs, we envision an extended language of TBFs that allows for complex formulas and nesting of formulas in temporal constraints. To this end, we present a language that extends propositional resp. FO logic with IA relations and provide semantics for it based on here-and-there (HT) logic as well as on Equilibrium logic. Furthermore, we lift a well-known tableau calculus for propositional HT logic to the temporal setting and report about an experimental prototype implementation. Based on these results, rich notions of diagnostic explanations from temporal behavior models may be developed.
A Abstract argumentation and Dung's framework are popular for modeling and evaluating arguments in artificial intelligence. We consider various counting problems in abstract argumentation under practical aspects. ...
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ISBN:
(纸本)9783031157073;9783031157066
A Abstract argumentation and Dung's framework are popular for modeling and evaluating arguments in artificial intelligence. We consider various counting problems in abstract argumentation under practical aspects. We revisit algorithms and establish a framework that employs dynamic programming on tree decompositions for counting extensions of abstract argumentation frameworks under admissible, stable, and complete semantics. We provide an empirical evaluation and investigate conditions under which our approach is useful.
Probabilistic logic Programs under the distribution semantics (PLPDS) do not allow statistical probabilistic statements of the form "90% of birds fly", which were defined "Type 1" statements by Hal...
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ISBN:
(纸本)9783031157073;9783031157066
Probabilistic logic Programs under the distribution semantics (PLPDS) do not allow statistical probabilistic statements of the form "90% of birds fly", which were defined "Type 1" statements by Halpern. In this paper, we add this kind of statements to PLPDS and introduce the PASTA ("Probabilistic Answer set programming for STAtistical probabilities") language. We translate programs in our new formalism into probabilistic answer set programs under the credal semantics. this approach differs from previous proposals, such as the one based on "probabilistic conditionals" as, instead of choosing a single model by making the maximum entropy assumption, we take into consideration all models and we assign probability intervals to queries. In this way we refrain from making assumptions and we obtain a more neutral framework. We also propose an inference algorithm and compare it with an existing solver for probabilistic answer set programs on a number of programs of increasing size, showing that our solution is faster and can deal with larger instances.
In this paper, we present a syntactic transformation, called the unfolding operator, that allows forgetting an atom in a logic program (under ASP semantics). the main advantage of unfolding is that, unlike other synta...
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ISBN:
(纸本)9783031157073;9783031157066
In this paper, we present a syntactic transformation, called the unfolding operator, that allows forgetting an atom in a logic program (under ASP semantics). the main advantage of unfolding is that, unlike other syntactic operators, it is always applicable and guarantees strong persistence, that is, the result preserves the same stable models with respect to any context where the forgotten atom does not occur. the price for its completeness is that the result is an expression that may contain the fork operator. Yet, we illustrate how, in some cases, the application of fork properties may allow us to reduce the fork to a logic program, even in conditions that could not be treated before using the syntactic methods in the literature.
Several AI problems can be conveniently modelled in ASP, and many of them require to enumerate solutions characterized by an optimality property that can be expressed in terms of subset-minimality with respect to some...
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ISBN:
(纸本)9783031157073;9783031157066
Several AI problems can be conveniently modelled in ASP, and many of them require to enumerate solutions characterized by an optimality property that can be expressed in terms of subset-minimality with respect to some objective atoms. In this context, solutions are often either (i) answer sets or (ii) sets of atoms that enforce the absence of answer sets on the ASP program at hand such sets are referred to as minimal unsatisfiable subsets (MUSes). In both cases, the required enumeration task is currently not supported by state-of-the-art ASP solvers.
Answer Set programming (ASP) is a well-established declarative AI formalism for knowledge representation and reasoning. ASP systems were successfully applied to both industrial and academic problems. Nonetheless, thei...
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ISBN:
(纸本)9783031157073;9783031157066
Answer Set programming (ASP) is a well-established declarative AI formalism for knowledge representation and reasoning. ASP systems were successfully applied to both industrial and academic problems. Nonetheless, their performance can be improved by embedding domain-specific heuristics into their solving process. However, the development of domain-specific heuristics often requires both a deep knowledge of the domain at hand and a good understanding of the fundamental working principles of the ASP solvers. In this paper, we investigate the use of deep learning techniques to automatically generate domain-specific heuristics for ASP solvers targeting the well-known graph coloring problem. Empirical results show that the idea is promising: the performance of the ASP solver WASP can be improved.
In this paper, we present a system, called xASP, for generating explanations that explain why an atom belongs to (or does not belong to) an answer set of a given program. the system can generate all possible explanati...
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ISBN:
(纸本)9783031157073;9783031157066
In this paper, we present a system, called xASP, for generating explanations that explain why an atom belongs to (or does not belong to) an answer set of a given program. the system can generate all possible explanations for a query without the need to simplify the program before computing explanations, i.e., it works with non-ground programs. these properties distinguish xASP from existing systems such as xClingo, DiscASP, exp(ASP(c)), and s(CASP), which also generate explanations for queries to logic programs under the answer set semantics but simplify and ground the programs (the three systems xClingo, DiscASP, exp(ASP(c))) or do not always generate all possible explanations (the system s(CASP)). In addition, the output of xASP is insensitive to syntactic variations such as the order conditions and the order of rules, which is also different from the output of s(CASP).
A Abstract dialectical frameworks (ADFs) are a well-studied generalisation of the prominent argumentation frameworks due to Phan Minh Dung. In this paper we propose to use reduced ordered binary decision diagrams (RoB...
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ISBN:
(纸本)9783031157073;9783031157066
A Abstract dialectical frameworks (ADFs) are a well-studied generalisation of the prominent argumentation frameworks due to Phan Minh Dung. In this paper we propose to use reduced ordered binary decision diagrams (RoBDDs) as a suitable representation of the acceptance conditions of arguments within ADFs. We first show that computational complexity of reasoning on ADFs represented by RoBDDs is milder than in the general case, with a drop of one level in the polynomial hierarchy. Furthermore, we present a framework to systematically define heuristics for search space exploitation, based on easily retrievable properties of RoBDDs and the recently proposed approach of weighted faceted navigation for answer set programming. Finally, we present preliminary experiments of an implementation of our approach showing promise both when compared to state-of-the-art solvers and when developing heuristics for reasoning.
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