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.
We report on using logic software in a novel course-format for an undergraduate logic course for students in computer science or artificialintelligence. Although being designed as the students' basic introduction...
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ISBN:
(纸本)9783031166815;9783031166808
We report on using logic software in a novel course-format for an undergraduate logic course for students in computer science or artificialintelligence. Although being designed as the students' basic introduction to the field of logic, the course features a novel structure and it adds some modern content, such as SAT and SMT solving, to the traditional and established topics, such as propositional logic and first order predicate logic. the novel course design is characterized by, among others, the integration of existing logic software into the teaching of logic. In this paper we focus on the module on first-order predicate logic and the use of the theorema system as a proof-tutor for the students. We report on statistical evaluation of data collected over two consecutive years of teaching this course. On the one hand, we asked for feedback of students on how helpful they felt the software support was. On the other hand, we evaluated their results in the exams during the course and their development over the entire teaching period. the performance in exams is then correlated with students' own perception of the helpfulness of software.
While remarkable recent developments in deep neural networks have significantly contributed to advancing the state-of-the-art in Computer Vision (CV), several studies have also shown their limitations and defects. In ...
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ISBN:
(纸本)9783031711664;9783031711671
While remarkable recent developments in deep neural networks have significantly contributed to advancing the state-of-the-art in Computer Vision (CV), several studies have also shown their limitations and defects. In particular, CV models often make systematic errors on important subsets of data called slices, which are groups of data sharing a set of attributes. the slice discovery problem involves detecting semantically meaningful slices on which the model performs poorly, called rare slices. We propose a modular Neurosymbolic AI approach whose distinct advantage is the extraction of human-readable logical rules that describe rare slices, and thus enhances explainability of CV models. To this end, we present a methodology to induce rare slice occurrences in a model. Experiments on datasets from our data generator leveraging on Super-CLEVR show that the approach can correctly identify rare slices and produce logical rules describing them. the rules can be fruitfully used to generate new training data to mend model behavior or may be integrated into the model to enhance its inference capabilities. (the code for reproducing our experiments is available as an online repository: https://***/kbs/nesy- ai/ilp4sd).
A Abstract argumentation and Dung's framework are popular for modeling and evaluating arguments in artificialintelligence. 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 artificialintelligence. 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.
Answer set programming (ASP) has long been used for modeling and solving hard search problems. Experience shows that the performance of ASP tools on different ASP encodings of the same problem may vary greatly from in...
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ISBN:
(纸本)9783031157073;9783031157066
Answer set programming (ASP) has long been used for modeling and solving hard search problems. Experience shows that the performance of ASP tools on different ASP encodings of the same problem may vary greatly from instance to instance and it is rarely the case that one encoding outperforms all others. We describe a system and its implementation that given a set of encodings and a training set of instances, builds performance models for the encodings, predicts the execution time of these encodings on new instances, and uses these predictions to select an encoding for solving.
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.
We propose a definition of common explanation for the label shared by a group of observations described as first order interpretations, and provide algorithms to enumerate minimal common explanations. this was motivat...
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ISBN:
(纸本)9783031450716;9783031450723
We propose a definition of common explanation for the label shared by a group of observations described as first order interpretations, and provide algorithms to enumerate minimal common explanations. this was motivated by explaining how performing some action, for instance a card played during a card game play, results in winning a maximum total reward at the end of the trajectory. As there are various ways to reach this reward, each associated to a group of trajectories, we propose to first build groups of trajectories and then build minimal common explanations for each group. the whole method is illustrated on a simplified Bridge game.
logical rules are a popular knowledge representation language in many domains. Recently, neural networks have been proposed to support the complex rule induction process. However, we argue that existing datasets and e...
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ISBN:
(数字)9783030974541
ISBN:
(纸本)9783030974541;9783030974534
logical rules are a popular knowledge representation language in many domains. Recently, neural networks have been proposed to support the complex rule induction process. However, we argue that existing datasets and evaluation approaches are lacking in various dimensions;for example, different kinds of rules or dependencies between rules are neglected. Moreover, for the development of neural approaches, we need large amounts of data to learn from and adequate, approximate evaluation measures. In this paper, we provide a tool for generating diverse datasets and for evaluating neural rule learning systems, including novel performance metrics.
Communicating Datalog Programs (CDPs) are a distributed computing model grounded on logicprogramming: networks of nodes perform Datalog-like computations, leveraging on information coming from incoming messages and d...
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ISBN:
(纸本)9783031450716;9783031450723
Communicating Datalog Programs (CDPs) are a distributed computing model grounded on logicprogramming: networks of nodes perform Datalog-like computations, leveraging on information coming from incoming messages and databases received from external services. In previous works, the decidability and complexity border of verification for different variants of CDPs was charted. In general, the problem is undecidable, but model-checking of CTL formulas specialized to the data-centric and distributed setting is decidable for CDPs where all data-sources, except the external inputs, are bounded. An intuitive explanation is that "a bounded state is unable to fully take advantage of an unbounded input", a formal justification is missing. However, we note that traditional CDPs have a limited capability of handling external inputs, i.e., they cannot directly compare two successive inputs or messages. thus, an alternative explanation is that an unbounded data-source does per se not cause undecidability, as long as the CDP cannot compare two successive instances.
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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