Distinguishing syntax from semantics is non-trivial and, some would argue, impossible. Given an appropriately-rich but still finitely-describable context, arguably, the semantics of a sentence in English might be precisely defined by a cleverly-constructed computer programme of finite size, thereby reducing semantics to a finite problem in syntax. Because such computer programmes are infeasible for the foreseeable future, we can distinguish syntax from semantics as follows. Semantics is ambiguous, whereas syntax can be fully defined in some description of finite length.
A doctrinal item has uncertainty, in at least two respects. First, as noted above, we are ultimately uncertain as to semantics: the meaning of a doctrinal item is inherently ambiguous. (Such ambiguity can often be ascribed to our uncertainty about the semantic context that is appropriate to the item. For example, in our two-coins scenario, we may believe that two tails is a ``winning position'' in some game being played, but we may not be sure that we know all the rules to this game.) Second, we have a higher-order uncertainty as to the validity of the item's presumed semantic content, when validity is judged under some contextually-appropriate definition. For example, we might be reading a daily horoscope without being convinced of its relevance to our life.
To summarise: doctrine is information that could be believed. Here I use the notion of ``belief'' to connote the partial certainty that distinguishes semantics from syntax, as well as to connote the need for some agent who might believe.
Note that computers are capable of manipulating doctrines. Humans can enter some doctrinal data into a computer, where it will be stored for an indefinite length of time. A computer can provide various retrieval mechanisms for previously-entered doctrines. It can even produce new doctrine, e.g. by combining two old doctrines in some ``believable'' way.
Computers are capable of storing information about degrees of belief, so in some limited sense we could say that a computer ``believes'' a doctrine. However, because computers operate by transforming data according to a finite set of syntactic rules, they lack the power to construe semantics. For this reason I require a human agent in any determination of belief, that is, I assert that a computer can manipulate, but not believe, doctrine.