diff --git a/index.bs b/index.bs index 6bdab5b..b70dff8 100644 --- a/index.bs +++ b/index.bs @@ -53,7 +53,7 @@ Talk: [BLOGIC](https://www.slideshare.net/PatHayes/blogic-iswc-2009-invited-talk Surfaces logic can be thought as an implementation of [Charles Sanders Peirce](https://en.wikipedia.org/wiki/Charles_Sanders_Peirce)'s [Existential Graphs](http://www.jfsowa.com/peirce/ms514.htm) in RDF. -An RDF surface is a kind of a sheet of paper on which RDF graphs can be written. +An RDF surface is a kind of sheet of paper on which RDF graphs can be written. All triples that are part of an RDF graph are then on this sheet of paper, including all [[URI]]s, literals and [Blank nodes](https://www.w3.org/TR/rdf11-mt/#blank-nodes). A sheet of paper can contain more than one RDF graph. An RDF graph can't be split @@ -86,7 +86,7 @@ A *positive surface* with one triple containing a blank node `[] a :City`, which
Two *positive surfaces*, one with the triple `[] a :City` (which means *"There is something that is a city"*), -and another one with the triple `[] a :Cat` (which means *"There is something is a cat"*). +and another one with the triple `[] a :Cat` (which means *"There is something that is a cat"*). blank surface @@ -113,7 +113,7 @@ For instance, the sheet of paper in Example 1 is an example of a **positive surf RDF triple written on this surface is interpreted as logical assertion (true). An empty sheet of positive paper is an empty claim and is treated as a logical tautology (true). -When there is there is more than one RDF triple on the surface, it is a logical conjunction (AND). +When there is more than one RDF triple on the surface, it is a logical conjunction (AND). If we interpret the sheets of paper with the black border in the examples above as positive surfaces, then they express: @@ -134,7 +134,7 @@ as a negative surface. An empty *negative surface* on the default positive surface expresses a logical contradiction. When one or more RDF graphs are written on a *negative* surface, they mean the negation of those RDF graphs. -A blank node on a negative surface is interpreted as an universal quantified variable. The reason is +A blank node on a negative surface is interpreted as a universal quantified variable. The reason is that: ``` @@ -184,7 +184,7 @@ Propositional logic using *positive* and *negative* surfaces. **First-order logic** First-order logic can be added to the RDF surfaces by interpreting a blank node as -an existential quantified variable and using the rule that a universal quantified variable can made from an +an existential quantified variable and using the rule that a universal quantified variable can be made from an existential quantified variable by placing it in an enclosing negative surface: - A blank node on a *positive surface* references an existential quantified variable. @@ -388,7 +388,7 @@ Surface {#Surface} ============================== Surfaces are written as triples where the `subject` is a list of zero or more blank nodes. -The `object` is a RDF graph or the `true` or `false` literal. The blank nodes in the +The `object` is an graph or the `true` or `false` literal. The blank nodes in the subject list are treated as marks on the object RDF graph. The `predicate` specifies the kind of surface. Any kind of surface may be used, but the following built-ins have special semantics: @@ -457,7 +457,7 @@ co-references is now limited to `ex:myThirdSurface`. ## Positive Surface ## {#PositiveSurface} A positive surface is an RDF Graph which claims that an RDF Graph on it is true. -This is the current default interperation of [RDF Semantics](https://www.w3.org/TR/rdf11-mt/). +This is the current default interpretation of [RDF Semantics](https://www.w3.org/TR/rdf11-mt/). When no surfaces are provided, an implicit positive surface is assumed in the RDF document.
@@ -582,7 +582,7 @@ When a blank node is marked on an odd-nested negative surface, it is interpreted as a universal quantified variable in the scope of the nested surface.
-The surface below should be interpreted as: "Every person knows Alice". +The surface below should be interpreted as: "Everything is a person and knows Alice". As a logical statement: diff --git a/index.html b/index.html index 282874e..ccbd42e 100644 --- a/index.html +++ b/index.html @@ -2098,7 +2098,7 @@

Pat Hayes in his 2009 ISWC Invited Talk: BLOGIC. RDF Surfaces logic can be thought as an implementation of Charles Sanders Peirce's Existential Graphs in RDF.

-

An RDF surface is a kind of a sheet of paper on which RDF graphs can be written. +

An RDF surface is a kind of sheet of paper on which RDF graphs can be written. All triples that are part of an RDF graph are then on this sheet of paper, including all [URI]s, literals and Blank nodes. A sheet of paper can contain more than one RDF graph. An RDF graph can’t be split over multiple sheets of paper. But, one can copy an RDF graph from one sheet of @@ -2120,9 +2120,9 @@

A positive surface with one triple containing a blank node [] a :City, which means "There is something that is a city".

blank surface

-
- Two positive surfaces, one with the triple [] a :City (which means "There is something that is a city"), -and another one with the triple [] a :Cat (which means "There is something is a cat"). +
+ Two positive surfaces, one with the triple [] a :City (which means "There is something that is a city"), +and another one with the triple [] a :Cat (which means "There is something that is a cat").

blank surface

One can copy these two RDFs graphs to a new surface. This will contain two graphs with two blank nodes:

@@ -2139,7 +2139,7 @@

positive surface (in this document, we use a paper with a black border as a positive surface). Any RDF triple written on this surface is interpreted as logical assertion (true). An empty sheet of positive paper is an empty claim and is treated as a logical tautology (true).

-

When there is there is more than one RDF triple on the surface, it is a logical conjunction (AND). +

When there is more than one RDF triple on the surface, it is a logical conjunction (AND). If we interpret the sheets of paper with the black border in the examples above as positive surfaces, then they express:

    @@ -2159,7 +2159,7 @@

    An empty negative surface on the default positive surface expresses a logical contradiction. When one or more RDF graphs are written on a negative surface, they mean the negation of those RDF graphs.

    -

    A blank node on a negative surface is interpreted as an universal quantified variable. The reason is +

    A blank node on a negative surface is interpreted as a universal quantified variable. The reason is that:

    NOT(∃ x : P(x)) ⇔ ∀ x : NOT(P(x))
    @@ -2206,7 +2206,7 @@

    First-order logic

    First-order logic can be added to the RDF surfaces by interpreting a blank node as -an existential quantified variable and using the rule that a universal quantified variable can made from an +an existential quantified variable and using the rule that a universal quantified variable can be made from an existential quantified variable by placing it in an enclosing negative surface:

    • @@ -2364,7 +2364,7 @@

      3. Surface

      Surfaces are written as triples where the subject is a list of zero or more blank nodes. -The object is a RDF graph or the true or false literal. The blank nodes in the +The object is an graph or the true or false literal. The blank nodes in the subject list are treated as marks on the object RDF graph. The predicate specifies the kind of surface. Any kind of surface may be used, but the following built-ins have special semantics:

      @@ -2415,7 +2415,7 @@

      3. <

3.1. Positive Surface

A positive surface is an RDF Graph which claims that an RDF Graph on it is true. -This is the current default interperation of RDF Semantics. +This is the current default interpretation of RDF Semantics. When no surfaces are provided, an implicit positive surface is assumed in the RDF document.

The two surfaces below are equal (because a double negation of a statement is the same as @@ -2507,8 +2507,8 @@

- The surface below should be interpreted as: "Every person knows Alice". +
+ The surface below should be interpreted as: "Everything is a person and knows Alice".

As a logical statement:

∀ _:X : _:X a :Person AND _:X :knows :Alice