Semantic graphs and truth

Responding to the previous post in a comment here Ed Ockham wonders how graph semantics can explain truth conditions. What would have to be true in order for 'someone crossed the Rubicon 2,000 years ago' to be true?

Here is more of the sketch.  I think there are two questions here.  The first is What would have to be the case in order for a person to judge that 'someone crossed the Rubicon 2,000 years ago'?  To answer this we need to suppose that everyone carries with them a 'background story', represented by a semantic graph.   The background story is everything the person believes.  The sentence 'someone crossed the Rubicon in 59BC' is represented by the following graph with an unlabelled object node.

If this matches a subgraph of the person's background story, either exactly or by matching a subgraph with a labelled object node, such as this one,

then they will judge the sentence true.  If, on the other hand, the background story contains the universal denials 'for all x, x did not cross the Rubicon in 59BC' or 'for all x, for all y, x did not cross the Rubicon in year y', represented by the following graphs,

then they will judge the sentence  false.  Otherwise, they will say that they just don't know whether the sentence is true or false.  Of course, their background story graph may match both patterns.  It may contain representations of inconsistent beliefs.  What they reply in these circumstances may well be indeterminate.

The second question is How does this relate to truth?  A background story's semantic graph could represent nothing but fiction.  Indeed, I very much suspect that the vast majority of my personal background story graph must derive from language, either heard or read.  But some must arise by direct aquaintance.  There must be a non-linguistic path by which external events, via the senses, cause the assembly of semantic graph elements.  Such elements must also play a role in planning our actions.   There is a sense in which they are rather like scientific hypotheses.  If they give rise to no 'surprises' as a result of our interactions with the world they acquire enhanced credibility.  This suggests that graph elements must have an associated 'degree of belief' factor, with those acquired by aquaintance receiving an initially high credibility, compared, say, with those acquired by exposure to speech or writing.  We can perhaps imagine the assertion and denial nodes of our graph distributed in some geometrical space with an inner core of aquaintance-derived nodes of high credibility surrounded by shells of linguistically-derived nodes of diminishing credibility.  None of this need be static.   An element of low credibility can move towards the core if corroborated by direct aquaintance or by a credible linguistic source.  And elements can be deleted altogether if they fail to cohere with high credibility elements.

Where does truth lie in all this?  Truth will be relative to the processes whereby we derive story elements from the senses.   These processes must be reliably consistent over space, time, and persons, for they generate the categories of object and property by which we conceptualise the world and communicate.