Extending the Automated Reasoning Toolbox

Due to the semi-decidable nature of first-order logic, it can be desirable to address a wider range of problems than the standard ones of satisfiability and derivability. We extend the automated reasoning toolbox by introducing three new tools for analysing problems in first-order logic. Infinox aims to show finite unsatisfiability, i.e. the absence of models with finite domains, and is a useful complement to finite model-finding. Infinox can also be used to reason about the relative sizes of model domains in sorted first-order logic. Monotonox uses a novel analysis that can identify sorts with extendable domains, improving on well-known existing translations between sorted and unsorted logic. This enables reasoning tools for unsorted logic to tackle problems in sorted logic. Conversely, finite model finders benefit from sort information which Monotonox can add to unsorted problems. Equalox, the third tool in our toolbox, can improve the per- formance of first-order provers on problems involving transitive relations. The insight is that first-order provers are poor at applying the transitivity axiom effectively, but that the problem can always be transformed to safely remove the transitivity axiom. Finally, we explore the field of computational linguistics as an application of automated reasoning. The tool Morfar uses a constraint solver to analyse the morphology of an input language. The result is a novel automatic method for segmentation and labelling that works well even when there is very little training data available

Handling Transitive Relations in First-Order Automated Reasoning

We present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and transitive relations in general. We show how such relations can be discovered syntactically in an input theory, and how they can be expressed in alternative ways. We experimentally evaluate different such ways on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain types of binary relations

Inferring Morphological Rules from Small Examples using 0/1 Linear Programming

We show how to express the problem of finding an optimal morpheme segmentation from a set of labelled words as a 0/1 linear programming problem, and how to build on this to analyse a language’s morphology. The result is an automatic method for segmentation and labelling that works well even when there is very little training data available

Data-driven models for predicting microbial water quality in the drinking water source using E. coli monitoring and hydrometeorological data

Rapid changes in microbial water quality in surface waters pose challenges for production of safe drinking water. If not treated to an acceptable level, microbial pathogens present in the drinking water can result in severe consequences for public health. The aim of this paper was to evaluate the suitability of data-driven models of different complexity for predicting the concentrations of E. coli in the river G\uf6ta \ue4lv at the water intake of the drinking water treatment plant in Gothenburg, Sweden. The objectives were to (i) assess how the complexity of the model affects the model performance; and (ii) identify relevant factors and assess their effect as predictors of E. coli levels. To forecast E. coli levels one day ahead, the data on laboratory measurements of E. coli and total coliforms, Colifast measurements of E. coli, water temperature, turbidity, precipitation, and water flow were used. The baseline approaches included Exponential Smoothing and ARIMA (Autoregressive Integrated Moving Average), which are commonly used univariate methods, and a naive baseline that used the previous observed value as its next prediction. Also, models common in the machine learning domain were included: LASSO (Least Absolute Shrinkage and Selection Operator) Regression and Random Forest, and a tool for optimising machine learning pipelines – TPOT (Tree-based Pipeline Optimization Tool). Also, a multivariate autoregressive model VAR (Vector Autoregression) was included. The models that included multiple predictors performed better than univariate models. Random Forest and TPOT resulted in higher performance but showed a tendency of overfitting. Water temperature, microbial concentrations upstream and at the water intake, and precipitation upstream were shown to be important predictors. Data-driven modelling enables water producers to interpret the measurements in the context of what concentrations can be expected based on the recent historic data, and thus identify unexplained deviations warranting further investigation of their origin

Extending the Automated Reasoning Toolbox

Due to the semi-decidable nature of first-order logic, it can be desirable to address a wider range of problems than the standard ones of satisfiability and derivability. We extend the automated reasoning toolbox by intro- ducing two new tools for analysing problems in first-order logic. Infinox is aimed at showing finite unsatisfiability, i.e. the absence of models with finite domains, and is a useful complement to finite model-finding. Monotonox, the second tool in our toolbox, uses a novel analysis that can identify sorts with extendable domains. Monotonox has successfully been used to improve on well-known existing translations between sorted and unsorted logic

Automated Inference of Finite Unsatisfiability

We present Infinox, an automated tool for analyzing first-order logic problems, aimed at showing finite unsatisfiability, i.e., the absence of models with finite domains. Finite satisfiability is not a decidable problem (only semi-decidable), which means that such a tool can never be complete. Nonetheless, our hope is that Infinox be a useful complement to finite model finders in practice. Infinox uses several different proof techniques for showing infinity of a set, each of which requires the identification of a function or a relation with particular properties. Infinox enumerates candidates to such functions and relations, and subsequently uses an automated theorem prover as a sub-procedure to try to prove the resulting proof obligations. We have evaluated Infinox on the relevant problems from the TPTP benchmark suite, and we are able to automatically show finite unsatisfiability for over 25% of these problems

Handling common transitive relations in first-order automated reasoning

We present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and reflexive, transitive relations. We show how such relations can be discovered syntactically in an input theory. We experimentally evaluate different treatments on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain binary relations

Local forecasts of electrc vehicles for grid planning purposes

Electrification of passenger vehicles is rapidly becoming the main alternative for decarbonizing transportation. The high power associated with charging of electric vehicles is likely to require actions from grid operators. Using machine learning and GIS analysis we produce forecasts of electric vehicles in very small cells, down to a few hundred meters for Norway. Using a baseline comparison, we find that a random forest model produces the overall lowest error, with a Mean Absolute Error of 14.0, and Mean Absolute Percentage Error of 33.9%. We find that both the existing vehicle fleet, and forecast shows that there is a large variation in electric vehicle adoption between cells. With knowledge where and when electric vehicles are adopted, grid operators can better plan their future investments related to electric vehicle charging, and thereby reduce investment costs