## 1 Introduction  
Bridges are vital elements of roadway and railway transportation infrastructure and they require timely decision-making to schedule Maintenance, Repair and Rehabilitation (MR&R) activities. To support the decision-making process, an increasing number of computer-aided Bridge Management Systems (BMSs) have been developed over the past two decades [1]. The main goal of the BMS is to establish an optimal operation strategy as a compromise between technical and social factors, such as maximization of network performance, minimization of life-cycle costs, and minimization of the probability of failure [2]. To establish such a strategy, it is essential to comprehend the long-term performance of a bridge, taking into account possible deterioration [3; 4]. For the prediction of the long-term performance of a bridge, most BMS software today uses statistical models based on condition ratings of bridge components or of an overall bridge, where the homogeneous Markov chain model is the most frequent [5]. In cases where condition prediction is purely based on condition ratings, the knowledge of how materials and elements are affected by the surrounding environment is not being fully employed [6]. Hence, implementing analytical deterioration models in BMSs, such as, e.g., the one describing the carbonation-induced corrosion, presents a suitable complement to current state. Moreover, significant research in the area of durability and benchmarking of material properties has recently been carried out, thus improving the accuracy of analytical deterioration models and their suitability for implementation in bridge management. The mentioned enhancements primarily refer to effort performed by the International Federation for Structural Concrete (_fib_) [7; 8; 9; 10]. The main aim of the article is to provide a framework that would utilize the information on the material, structural and environmental properties of bridges while still using the outcomes of visual inspection. This primarily refers to the Principal Inspection, in contrast to other possible visual inspection types such as the Routine Inspection, Special Inspection, etc. To do so, the information collected during visual inspection should be related to features such as surface characteristics, visible deformation, cracks, spalling, corrosion, etc. Furthermore, the results of the inspection need to be expressed in terms of a qualitative grading of structural condition for possible degradation (e.g., none, minor, moderate, severe, etc. ), accompanied by quantitative grading in the form of condition rating. Condition ratings are usually assigned to different scales by different organizations, and as such, they define the condition state (CS) of the structure or its elements. Along with its focus on the framework, the article includes an overview on the semi-Markov process as an alternative to the homogeneous Markov chain. There are several assumptions taken in order to simplify the use of the homogeneous Markov chain, which can be found described in [11; 12]. Some of these assumptions restrict use and decrease the accuracy, and can be seen as shortcomings of the model. Therefore, in the last few decades, dozens of different condition prediction models have been developed in order to serve as an enhancement and alternative to the simple homogeneous Markov chain. One path led to using Bayesian optimization techniques [13; 14; 15; 16] and artificial intelligence techniques such as Artificial Neural Network (ANN) [17; 18; 19], fuzzy logic [20; 21], genetic algorithm [22; 23; 24], and so on. However, mostly, the enhancements have been focused on using the Markov property in different types of models, such as the hidden Markov chain [25; 26], partially observable Markov process [26; 27; 28; 29], etc. Still, some of the shortcomings of the homogeneous Markov chain, such as stationarity of transition probabilities, non-consideration of past deterioration path, and non-consideration of actual structural and material properties, have remained only marginally addressed.