Interval Logic Tensor Networks

In this paper, we introduce Interval Real Logic (IRL), a two-sorted logic that interprets knowledge such as sequential properties (traces) and event properties using sequences of real-featured data. We interpret connectives using fuzzy logic, event durations using trapezoidal fuzzy intervals, and fuzzy temporal relations using relationships between the intervals' areas. We propose Interval Logic Tensor Networks (ILTN), a neuro-symbolic system that learns by propagating gradients through IRL. In order to support effective learning, ILTN defines smoothened versions of the fuzzy intervals and temporal relations of IRL using softplus activations. We show that ILTN can successfully leverage knowledge expressed in IRL in synthetic tasks that require reasoning about events to predict their fuzzy durations. Our results show that the system is capable of making events compliant with background temporal knowledge

Logic tensor networks for semantic image interpretation

Semantic Image Interpretation (SII) is the task of extracting structured semantic descriptions from images. It is widely agreed that the combined use of visual data and background knowledge is of great importance for SII. Recently, Statistical Relational Learning (SRL) approaches have been developed for reasoning under uncertainty and learning in the presence of data and rich knowledge. Logic Tensor Networks (LTNs) are a SRL framework which integrates neural networks with first-order fuzzy logic to allow (i) efficient learning from noisy data in the presence of logical constraints, and (ii) reasoning with logical formulas describing general properties of the data. In this paper, we develop and apply LTNs to two of the main tasks of SII, namely, the classification of an image's bounding boxes and the detection of the relevant part-of relations between objects. To the best of our knowledge, this is the first successful application of SRL to such SII tasks. The proposed approach is evaluated on a standard image processing benchmark. Experiments show that background knowledge in the form of logical constraints can improve the performance of purely data-driven approaches, including the state-of-theart Fast Region-based Convolutional Neural Networks (Fast R-CNN). Moreover, we show that the use of logical background knowledge adds robustness to the learning system when errors are present in the labels of the training data

Deterministic and Probabilistic Boolean Control Networks and their application to Gene Regulatory Networks

This thesis focuses on Deterministic and Probabilistic Boolean Control Networks and their application to some specific Gene Regulatory Networks. At first, some introductory materials about Boolean Logic, Left Semi-tensor Product and Probability are presented in order to explain in detail the concepts of Boolean Networks, Boolean Control Networks, Probabilistic Boolean Networks and Probabilistic Boolean Control Networks. These networks can be modelled in state-space and their representation, obtained by means of the left semi-tensor product, is called algebraic form. Subsequently, the thesis concentrates on presenting the fundamental properties of these networks such as the classical Systems Theory properties of stability, reachability, controllability and stabilisation. Afterwards, the attention is drawn towards the comparison between deterministic and probabilistic boolean networks. Finally, two examples of Gene Regulatory Networks are modelled and analysed by means of a Boolean Network and a Probabilistic Boolean Network.This thesis focuses on Deterministic and Probabilistic Boolean Control Networks and their application to some specific Gene Regulatory Networks. At first, some introductory materials about Boolean Logic, Left Semi-tensor Product and Probability are presented in order to explain in detail the concepts of Boolean Networks, Boolean Control Networks, Probabilistic Boolean Networks and Probabilistic Boolean Control Networks. These networks can be modelled in state-space and their representation, obtained by means of the left semi-tensor product, is called algebraic form. Subsequently, the thesis concentrates on presenting the fundamental properties of these networks such as the classical Systems Theory properties of stability, reachability, controllability and stabilisation. Afterwards, the attention is drawn towards the comparison between deterministic and probabilistic boolean networks. Finally, two examples of Gene Regulatory Networks are modelled and analysed by means of a Boolean Network and a Probabilistic Boolean Network

Semantics, Modelling, and the Problem of Representation of Meaning -- a Brief Survey of Recent Literature

Over the past 50 years many have debated what representation should be used to capture the meaning of natural language utterances. Recently new needs of such representations have been raised in research. Here I survey some of the interesting representations suggested to answer for these new needs.Comment: 15 pages, no figure