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Harry is a GE, from your assertions. GE is both a class and an individual; so GE appears in other statements as well, and that's multiplying the answers you're seeing. It's analogous as joining across tables where the join value matches multiple rows in one of the tables involved.

I can quote RDFS, and considering OWL should follow from that, I don't expect any difference there:

If a class C is a subclass of a class C', then all instances of C will also be instances of C'. The rdfs:subClassOf property may be used to state that one class is a subclass of another.

Class inheritance axioms in RDFS are built so that a contradiction can never occur, thus a statement like this can only be "additive" in a sense. Additionally, from the nature of triples in RDF, we know that A rdfs:subClassOf B, C. means A rdfs:subClassOf B. A rdfs:subClassOf C..

Expressed in the language of sets, such a construction means A ⊆ B ∧ A ⊆ C. Any member of A is also a member of B, and any member of A is also a member of C, thus any member of A must be a member of both B and C. We can see that A ⊆ (B ∩ C), from the duality of set and logical operators.

Expressed equivalently, any member of B not found in C must also not be in A (and the same for B and C swapped).

Here is my approach based on this answer. See also this notebook for outputs.

There is an alternative implementation of OWLAPI-v5 that provides a direct way to work with underlying RDF data - ONT-API (by the way, RDF based Protege version also exists). If working via OWLAPI interface for two operands it produces a single triple.

Also it is possible to copy ontology between ont-api manager and owl-api-impl managers, if you prefer to store the data in the form of OWL axioms and need to solve only this particular problem with serialization.

example:

I think the first thing to be aware of is that equivalence, say D equivalentClass E, is an abbreviation for D subClassOf E and E subClassOf D. The semantics of subClassOf is subset. This means that the set D is a subset of set E and set E is a subset of D, which means set D and set E are exactly the same set. We say they are equivalent.

Note now the semantics of subClassOf. If I know F subClassOf E and G subClassOf E, what can I say about how F and G relates to each other? Absolutely nothing. It is a bit like knowing a bicycle and a truck are both vehicles. That does not make a bicycle a truck or a truck a bicycle, though both are vehicles.

Thus, in your example, A can be expanded to the 2 axioms

A subClassOf (a_to_b some B) and (a_to_c some C)

(a_to_b some B) and (a_to_c some C) subClassOf A

Answers to your questions:

(a) With the assertions for x as you have it, we can see that x is indeed an instance of A. However, there is no information wrt x that makes it possible for us to say x is of type A2. All we know is that both x and A2 are subclasses of (a_to_b some B) and (a_to_c some C).

(b) This is due to the Open World Assumption, which means the reasoner does not make any assumptions based on the absence of information. If you have not stated explicitly that y has no a_to_b relation to B, it will assume that an a_to_b relation exists but is merely not known. This is as opposed to the closed world assumption made by databases usually. I.e., if no employer information exists for a client the assumption is often made that the client is not employed.

You can state that y has no a_to_b relation by stating that a_to_b max 0 B. The reasoner will then give an inconsistency.

(c1) yes, but these may not be known currently due to the open world assumption.

(c2) yes, based on the semantics of equivalence

(c3) yes.

This is not true for A2 because it is merely a subclass rather than all things that have a relation a_to_b with an instance of B and have a relation a_to_C with an instance of C.

When to use equivalent vs subClassOf

Equivalence is used for definitions. That is when you want to state the necessary and sufficient conditions for something to be called an A (from your example).

SubClassOf is used when you want to define a hierarchy from most general to most specific. I.e., it is typically what you see in taxonomies and in programming you will see it as object oriented class hierarchies.

In general a set of axioms has an infinite amout of entailments. See for example this paper. For this reason reasoners restrict inferences to known classes (not anonymous classes). I suspect this holds true for rules as well.

I therefore suggest you add a class NoRain that you set equivalent to has_weather 0 Rain and change your SWRL rule to use the class NoRain.

You can import http://www.w3.org/ns/ssn/systems/, which itself imports http://www.w3.org/ns/ssn/.

You have this structure

There is no inferred axiom generator that materialises the sameAs relations. You could write one yourself, based e.g., on InferredPropertyAssertionGenerator, or you can open an issue on the OWLAPI GitHub repo for the functionality to be added to the library.