In Bitcoin, if a miner is able to solve a computationally hard problem called proof of work, it will receive an amount of bitcoin as a reward which is the sum of the fees for the transactions included in a block plus an amount inversely proportional to the number of blocks discovered so far. At the moment of writing, the block reward is several orders of magnitude greater than the sum of transaction fees. Usually, miners try to collect the largest reward by including transactions associated with high fees. The main purpose of transaction fees is to prevent network spamming. However, they are also used to prioritize transactions. In order to use the minimum amount of fees, users usually have to find a compromise between fees and urgency of a transaction. In this paper, we develop a probabilistic logic model to experimentally analyze how fees affect confirmation time and miner’s revenue and to predict if an increase of average fees will generate a situation when the miner gets more reward by not following the protocol.

Probabilistic logic programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions of random variables. Here, we introduce a new class of probabilistic logic programs, namely probabilisticoptimizablelogic programs, and we provide an effective algorithm to find the best assignment to probabilities of random variables, such that a set of constraints is satisfied and an objective function is optimized.

In 1990, Halpern proposed the distinction between Type 1 and Type 2 statements: the former express statistical information about a domain of interest while the latter define a degree of belief. An example of Type 1 statement is “30% of the elements of a domain share the same property” while an example of Type 2 statement is “the element x has the property y with probability p”. Recently, Type 1 statements were given an interpretation in terms of probabilistic answer set programs under the credal semantics in the PASTA framework. The algorithm proposed for inference requires the enumeration of all the answer sets of a given program, and so it is impractical for domains of not trivial size. The field of lifted inference aims to identify programs where inference can be computed without grounding the program. In this paper, we identify some classes of PASTA programs for which we apply lifted inference and develop compact formulas to compute the probability bounds of a query without the need to generate all the possible answer sets.