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Latest Research Publications:
1.
Everett L, Morris E, Meyer T. Explanation for KLM-Style Defeasible Reasoning. In: Artificial Intelligence Research. SACAIR 2021. 1551st ed. Cham: Springer; 2022. doi:10.1007/978-3-030-95070-5_13.
Explanation services are a crucial aspect of symbolic reasoning systems but they have not been explored in detail for defeasible formalisms such as KLM. We evaluate prior work on the topic with a focus on KLM propositional logic and find that a form of defeasible explanation initially described for Rational Closure which we term weak justification can be adapted to Relevant and Lexicographic Closure as well as described in terms of intuitive properties derived from the KLM postulates. We also consider how a more general definition of defeasible explanation known as strong explanation applies to KLM and propose an algorithm that enumerates these justifications for Rational Closure.
@inbook{426,
author = {Lloyd Everett, Emily Morris, Tommie Meyer},
title = {Explanation for KLM-Style Defeasible Reasoning},
abstract = {Explanation services are a crucial aspect of symbolic reasoning systems but they have not been explored in detail for defeasible formalisms such as KLM. We evaluate prior work on the topic with a focus on KLM propositional logic and find that a form of defeasible explanation initially described for Rational Closure which we term weak justification can be adapted to Relevant and Lexicographic Closure as well as described in terms of intuitive properties derived from the KLM postulates. We also consider how a more general definition of defeasible explanation known as strong explanation applies to KLM and propose an algorithm that enumerates these justifications for Rational Closure.},
year = {2022},
journal = {Artificial Intelligence Research. SACAIR 2021.},
edition = {1551},
publisher = {Springer},
address = {Cham},
isbn = {978-3-030-95069-9},
url = {https://link.springer.com/book/10.1007/978-3-030-95070-5},
doi = {10.1007/978-3-030-95070-5_13},
}
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Latest Research Publications:
1.
Mouton C, Davel MH. Exploring layerwise decision making in DNNs. Communications in Computer and Information Science. 2022;1551. doi:https://doi.org/10.1007/978-3-030-95070-5_10.
While deep neural networks (DNNs) have become a standard architecture for many machine learning tasks, their internal decision-making process and general interpretability is still poorly understood. Conversely, common decision trees are easily interpretable and theoretically well understood. We show that by encoding the discrete sample activation values of nodes as a binary representation, we are able to extract a decision tree explaining the classification procedure of each layer in a ReLU-activated multilayer perceptron (MLP). We then combine these decision trees with existing feature attribution techniques in order to produce an interpretation of each layer of a model. Finally, we provide an analysis of the generated interpretations, the behaviour of the binary encodings and how these relate to sample groupings created during the training process of the neural network.
@article{479,
author = {Coenraad Mouton, Marelie Davel},
title = {Exploring layerwise decision making in DNNs},
abstract = {While deep neural networks (DNNs) have become a standard architecture for many machine learning tasks, their internal decision-making process and general interpretability is still poorly understood. Conversely, common decision trees are easily interpretable and theoretically well understood. We show that by encoding the discrete sample activation values of nodes as a binary representation, we are able to extract a decision tree explaining the classification procedure of each layer in a ReLU-activated multilayer perceptron (MLP). We then combine these decision trees with existing feature attribution techniques in order to produce an interpretation of each layer of a model. Finally, we provide an analysis of the generated interpretations, the behaviour of the binary encodings and how these relate to sample groupings created during the training process of the neural network.},
year = {2022},
journal = {Communications in Computer and Information Science},
volume = {1551},
pages = {140 - 155},
publisher = {Artificial Intelligence Research (SACAIR 2021)},
doi = {https://doi.org/10.1007/978-3-030-95070-5_10},
}
1.
Myburgh JC, Mouton C, Davel MH. Tracking translation invariance in CNNs. Communications in Computer and Information Science. 2020;1342. doi:https://doi.org/10.1007/978-3-030-66151-9_18.
Although Convolutional Neural Networks (CNNs) are widely used, their translation invariance (ability to deal with translated inputs) is still subject to some controversy. We explore this question using translation-sensitivity maps to quantify how sensitive a standard CNN is to a translated input. We propose the use of cosine similarity as sensitivity metric over Euclidean distance, and discuss the importance of restricting the dimensionality of either of these metrics when comparing architectures. Our main focus is to investigate the effect of different architectural components of a standard CNN on that network’s sensitivity to translation. By varying convolutional kernel sizes and amounts of zero padding, we control the size of the feature maps produced, allowing us to quantify the extent to which these elements influence translation invariance. We also measure translation invariance at different locations within the CNN to determine the extent to which convolutional and fully connected layers, respectively, contribute to the translation invariance of a CNN as a whole. Our analysis indicates that both convolutional kernel size and feature map size have a systematic influence on translation invariance. We also see that convolutional layers contribute less than expected to translation invariance, when not specifically forced to do so.
@article{485,
author = {Johannes Myburgh, Coenraad Mouton, Marelie Davel},
title = {Tracking translation invariance in CNNs},
abstract = {Although Convolutional Neural Networks (CNNs) are widely used, their translation invariance (ability to deal with translated inputs) is still subject to some controversy. We explore this question using translation-sensitivity maps to quantify how sensitive a standard CNN is to a translated input. We propose the use of cosine similarity as sensitivity metric over Euclidean distance, and discuss the importance of restricting the dimensionality of either of these metrics when comparing architectures. Our main focus is to investigate the effect of different architectural components of a standard CNN on that network’s sensitivity to translation. By varying convolutional kernel sizes and amounts of zero padding, we control the size of the feature maps produced, allowing us to quantify the extent to which these elements influence translation invariance. We also measure translation invariance at different locations within the CNN to determine the extent to which convolutional and fully connected layers, respectively, contribute to the translation invariance of a CNN as a whole. Our analysis indicates that both convolutional kernel size and feature map size have a systematic influence on translation invariance. We also see that convolutional layers contribute less than expected to translation invariance, when not specifically forced to do so.},
year = {2020},
journal = {Communications in Computer and Information Science},
volume = {1342},
pages = {282-295},
publisher = {Southern African Conference for Artificial Intelligence Research},
isbn = {978-3-030-66151-9},
doi = {https://doi.org/10.1007/978-3-030-66151-9_18},
}
1.
Mouton C, Myburgh JC, Davel MH. Stride and translation invariance in CNNs. Communications in Computer and Information Science . 2020;1342. doi:https://doi.org/10.1007/978-3-030-66151-9_17.
Convolutional Neural Networks have become the standard for image classification tasks, however, these architectures are not invariant to translations of the input image. This lack of invariance is attributed to the use of stride which subsamples the input, resulting in a loss of information, and fully connected layers which lack spatial reasoning. We show that stride can greatly benefit translation invariance given that it is combined with sufficient similarity between neighbouring pixels, a characteristic which we refer to as local homogeneity. We also observe that this characteristic is dataset-specific and dictates the relationship between pooling kernel size and stride required for translation invariance. Furthermore we find that a trade-off exists between generalization and translation invariance in the case of pooling kernel size, as larger kernel sizes lead to better invariance but poorer generalization. Finally we explore the efficacy of other solutions proposed, namely global average pooling, anti-aliasing, and data augmentation, both empirically and through the lens of local homogeneity.
@article{486,
author = {Coenraad Mouton, Johannes Myburgh, Marelie Davel},
title = {Stride and translation invariance in CNNs},
abstract = {Convolutional Neural Networks have become the standard for image classification tasks, however, these architectures are not invariant to translations of the input image. This lack of invariance is attributed to the use of stride which subsamples the input, resulting in a loss of information, and fully connected layers which lack spatial reasoning. We show that stride can greatly benefit translation invariance given that it is combined with sufficient similarity between neighbouring pixels, a characteristic which we refer to as local homogeneity. We also observe that this characteristic is dataset-specific and dictates the relationship between pooling kernel size and stride required for translation invariance. Furthermore we find that a trade-off exists between generalization and translation invariance in the case of pooling kernel size, as larger kernel sizes lead to better invariance but poorer generalization. Finally we explore the efficacy of other solutions proposed, namely global average pooling, anti-aliasing, and data augmentation, both empirically and through the lens of local homogeneity.},
year = {2020},
journal = {Communications in Computer and Information Science},
volume = {1342},
pages = {267-281},
publisher = {Southern African Conference for Artificial Intelligence Research},
address = {South Africa},
isbn = {978-3-030-66151-9},
doi = {https://doi.org/10.1007/978-3-030-66151-9_17},
}
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DEGREES LINKED TO THIS RESEARCH GROUP: 2021 - current PhD (Philosophy)
“The Role of the Board in Artificial Intelligence Ethics and Governance – A Case
for JSE Listed Companies”
Workshop attended:
1) 23 March 2021 Catalysing cooperation: Working Together Across AI
Governance Initiatives
2) 13 April 2021 ICGAI: Meaning Inclusivity in Governing AI Revolution
3) 19 May 2021 Digital Insight: Bridging the Trust Gap – How to Govern AI
4) 17 June 2021 Intelligent Decisions powered by AI: A critical tool for Digital
Government
5) 23 June Artificial Intelligence: How Secure are your ML and AI projects and
How human bias limits
6) 23 September 2021 Applying AI to tackle the Climate Crisis
Publication:
Who is responsible? AI vs corporate governance and SA law
https://www.bizcommunity.com/Article/196/547/208888.html
“The Role of the Board in Artificial Intelligence Ethics and Governance – A Case
for JSE Listed Companies”
Workshop attended:
1) 23 March 2021 Catalysing cooperation: Working Together Across AI
Governance Initiatives
2) 13 April 2021 ICGAI: Meaning Inclusivity in Governing AI Revolution
3) 19 May 2021 Digital Insight: Bridging the Trust Gap – How to Govern AI
4) 17 June 2021 Intelligent Decisions powered by AI: A critical tool for Digital
Government
5) 23 June Artificial Intelligence: How Secure are your ML and AI projects and
How human bias limits
6) 23 September 2021 Applying AI to tackle the Climate Crisis
Publication:
Who is responsible? AI vs corporate governance and SA law
https://www.bizcommunity.com/Article/196/547/208888.html
Latest Research Publications:
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I am broadly interested in Artificial Intelligence for Development (AI4D), with my research focus being agent-based computing and machine learning for healthcare. My research is conducted within the Adaptive and Cognitive Systems Lab, part of South Africa's Centre for Artificial Intelligence Research (CAIR) network. I'm supervised by A/Prof. Deshen Moodley. Prior to this, I graduated with Distinction from the University of Manchester, where I earned an MSc in Advanced Computer Science with a specialization in AI.
Latest Research Publications:
1.
Wanyana T, Nzomo M, Price CS, Moodley D. Combining Machine Learning and Bayesian Networks for ECG Interpretation and Explanation. In: Proceedings of the 8th International Conference on Information and Communication Technologies for Ageing Well and e-Health - ICT4AWE. INSTICC: SciTePress; 2022. doi:https://doi.org/10.5220/0011046100003188.
We explore how machine learning (ML) and Bayesian networks (BNs) can be combined in a personal health agent (PHA) for the detection and interpretation of electrocardiogram (ECG) characteristics. We propose a PHA that uses ECG data from wearables to monitor heart activity, and interprets and explains the observed readings. We focus on atrial fibrillation (AF), the commonest type of arrhythmia. The absence of a P-wave in an ECG is the hallmark indication of AF. Four ML models are trained to classify an ECG signal based on the presence or absence of the P-wave: multilayer perceptron (MLP), logistic regression, support vector machine, and random forest. The MLP is the best performing model with an accuracy of 89.61% and an F1 score of 88.68%. A BN representing AF risk factors is developed based on expert knowledge from the literature and evaluated using Pitchforth and Mengersen’s validation framework. The P-wave presence or absence as determined by the ML model is input into the BN. The PHA is evaluated using sample use cases to illustrate how the BN can explain the occurrence of AF using diagnostic reasoning. This gives the most likely AF risk factors for the individual
@inbook{478,
author = {Tezira Wanyana, Mbithe Nzomo, C. Sue Price, Deshen Moodley},
title = {Combining Machine Learning and Bayesian Networks for ECG Interpretation and Explanation},
abstract = {We explore how machine learning (ML) and Bayesian networks (BNs) can be combined in a personal health agent (PHA) for the detection and interpretation of electrocardiogram (ECG) characteristics. We propose a PHA that uses ECG data from wearables to monitor heart activity, and interprets and explains the observed readings. We focus on atrial fibrillation (AF), the commonest type of arrhythmia. The absence of a P-wave in an ECG is the hallmark indication of AF. Four ML models are trained to classify an ECG signal based on the presence or absence of the P-wave: multilayer perceptron (MLP), logistic regression, support vector machine, and random forest. The MLP is the best performing model with an accuracy of 89.61% and an F1 score of 88.68%. A BN representing AF risk factors is developed based on expert knowledge from the literature and evaluated using Pitchforth and Mengersen’s validation framework. The P-wave presence or absence as determined by the ML model is input into the BN. The PHA is evaluated using sample use cases to illustrate how the BN can explain the occurrence of AF using diagnostic reasoning. This gives the most likely AF risk factors for the individual},
year = {2022},
journal = {Proceedings of the 8th International Conference on Information and Communication Technologies for Ageing Well and e-Health - ICT4AWE},
pages = {81-92},
publisher = {SciTePress},
address = {INSTICC},
isbn = {978-989-758-566-1},
doi = {https://doi.org/10.5220/0011046100003188},
}
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Latest Research Publications:
1.
Oosthuizen AJ, Davel MH, Helberg A. Multi-Layer Perceptron for Channel State Information Estimation: Design Considerations. In: Southern Africa Telecommunication Networks and Applications Conference (SATNAC). Fancourt, George; 2022.
The accurate estimation of channel state information (CSI) is an important aspect of wireless communications. In this paper, a multi-layer perceptron (MLP) is developed as a CSI estimator in long-term evolution (LTE) transmission conditions. The representation of the CSI data is investigated in conjunction with batch normalisation and the representational ability of MLPs. It is found that discontinuities in the representational feature space can cripple an MLP’s ability to accurately predict CSI when noise is present. Different ways in which to mitigate this effect are analysed and a solution developed, initially in the context of channels that are only affected by additive white
Guassian noise. The developed architecture is then applied to more complex channels with various delay profiles and Doppler spread. The performance of the proposed MLP is shown to be comparable with LTE minimum mean squared error (MMSE), and to outperform least square (LS) estimation over a range of channel conditions.
@{491,
author = {Andrew Oosthuizen, Marelie Davel, Albert Helberg},
title = {Multi-Layer Perceptron for Channel State Information Estimation: Design Considerations},
abstract = {The accurate estimation of channel state information (CSI) is an important aspect of wireless communications. In this paper, a multi-layer perceptron (MLP) is developed as a CSI estimator in long-term evolution (LTE) transmission conditions. The representation of the CSI data is investigated in conjunction with batch normalisation and the representational ability of MLPs. It is found that discontinuities in the representational feature space can cripple an MLP’s ability to accurately predict CSI when noise is present. Different ways in which to mitigate this effect are analysed and a solution developed, initially in the context of channels that are only affected by additive white
Guassian noise. The developed architecture is then applied to more complex channels with various delay profiles and Doppler spread. The performance of the proposed MLP is shown to be comparable with LTE minimum mean squared error (MMSE), and to outperform least square (LS) estimation over a range of channel conditions.},
year = {2022},
journal = {Southern Africa Telecommunication Networks and Applications Conference (SATNAC)},
pages = {94 - 99},
month = {08/2022},
address = {Fancourt, George},
}
1.
Oosthuizen AJ, Davel MH, Helberg A. Exploring CNN-based automatic modulation classification using small modulation sets. In: Southern Africa Telecommunication Networks and Applications Conference. South Africa; 2021. https://www.satnac.org.za/proceedings.
We investigate the effect of a reduced modulation scheme pool on a CNN-based automatic modulation classifier. Similar classifiers in literature are typically used to classify sets of five or more different modulation types [1] [2], whereas our
analysis is of a CNN classifier that classifies between two modulation types, 16-QAM and 8-PSK, only. While implementing the network, we observe that the network’s classification accuracy improves for lower SNR instead of reducing as expected. This analysis exposes characteristics of such classifiers that can be used to improve CNN classifiers on larger sets of modulation types. We show that presenting the SNR data as an extra data point to the network can significantly increase classification accuracy.
@{481,
author = {Andrew Oosthuizen, Marelie Davel, Albert Helberg},
title = {Exploring CNN-based automatic modulation classification using small modulation sets},
abstract = {We investigate the effect of a reduced modulation scheme pool on a CNN-based automatic modulation classifier. Similar classifiers in literature are typically used to classify sets of five or more different modulation types [1] [2], whereas our
analysis is of a CNN classifier that classifies between two modulation types, 16-QAM and 8-PSK, only. While implementing the network, we observe that the network’s classification accuracy improves for lower SNR instead of reducing as expected. This analysis exposes characteristics of such classifiers that can be used to improve CNN classifiers on larger sets of modulation types. We show that presenting the SNR data as an extra data point to the network can significantly increase classification accuracy.},
year = {2021},
journal = {Southern Africa Telecommunication Networks and Applications Conference},
pages = {20 - 24},
month = {21/11/2021 - 23/11/2021},
address = {South Africa},
url = {https://www.satnac.org.za/proceedings},
}
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Latest Research Publications:
1.
Casini G, Meyer T, Paterson-Jones G. KLM-Style Defeasibility for Restricted First-Order Logic. In: 19th International Workshop on Non-Monotonic Reasoning. Online; 2021. https://drive.google.com/open?id=1WSIl3TOrXBhaWhckWN4NLXoD9AVFKp5R.
We extend the KLM approach to defeasible reasoning to be applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide an appropriate semantics for it, and present a representation result that characterises the semantic description of defeasibility in terms of the rationality postulates. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by Rational Closure as it is defined for defeasible propositional logic and defeasible description logics. We show that this form of defeasible entailment is rational in the sense that it adheres to our rationality postulates. The work in this paper is the first step towards our ultimate goal of introducing KLM-style defeasible reasoning into the family of Datalog+/- ontology languages.
@{429,
author = {Giovanni Casini, Tommie Meyer, Guy Paterson-Jones},
title = {KLM-Style Defeasibility for Restricted First-Order Logic},
abstract = {We extend the KLM approach to defeasible reasoning to be applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide an appropriate semantics for it, and present a representation result that characterises the semantic description of defeasibility in terms of the rationality postulates. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by Rational Closure as it is defined for defeasible propositional logic and defeasible description logics. We show that this form of defeasible entailment is rational in the sense that it adheres to our rationality postulates. The work in this paper is the first step towards our ultimate goal of introducing KLM-style defeasible reasoning into the family of Datalog+/- ontology languages.},
year = {2021},
journal = {19th International Workshop on Non-Monotonic Reasoning},
pages = {184-193},
month = {03/11/2021-05/11/2021},
address = {Online},
url = {https://drive.google.com/open?id=1WSIl3TOrXBhaWhckWN4NLXoD9AVFKp5R},
}
1.
Paterson-Jones G, Meyer T. A Boolean Extension of KLM-style Conditional Reasoning. In: First Southern African Conference for AI Research (SACAIR 2020). Muldersdrift, South Africa: Springer; 2020. doi:10.1007/978-3-030-66151-9_15.
Propositional KLM-style defeasible reasoning involves extending propositional logic with a new logical connective that can express defeasible (or conditional) implications, with semantics given by ordered structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.
@{413,
author = {Guy Paterson-Jones, Tommie Meyer},
title = {A Boolean Extension of KLM-style Conditional Reasoning},
abstract = {Propositional KLM-style defeasible reasoning involves extending propositional logic with a new logical connective that can express defeasible (or conditional) implications, with semantics given by ordered structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.},
year = {2020},
journal = {First Southern African Conference for AI Research (SACAIR 2020)},
pages = {236-252},
month = {22/02/2021-26/02/2021},
publisher = {Springer},
address = {Muldersdrift, South Africa},
isbn = {978-3-030-66151-9},
url = {https://link.springer.com/book/10.1007/978-3-030-66151-9},
doi = {10.1007/978-3-030-66151-9_15},
}
1.
Paterson-Jones G, Casini G, Meyer T. BKLM - An expressive logic for defeasible reasoning. 18th International Workshop on Non-Monotonic Reasoning. 2020.
Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique.
In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.
@misc{383,
author = {Guy Paterson-Jones, Giovanni Casini, Tommie Meyer},
title = {BKLM - An expressive logic for defeasible reasoning},
abstract = {Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique.
In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.},
year = {2020},
journal = {18th International Workshop on Non-Monotonic Reasoning},
month = {12/09/2020-24/09/2020},
}
