https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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dc:description "analysis.py enumerates all 2305 one- and two-rule systems over {A,B} with lhs length 1-3 and strictly shorter rhs, classifies each syntactically as non-overlapping (37 systems; lhs sets {A}, {B}, {A,B}, {AB}, {BA}, {AAB}, {ABB}, {BAA}, {BBA}) or overlapping (2268), and for each of the 62 initial strings of length 1-5 generates every complete evolution by depth-first search over all possible replacement choices, tracking element identities so that each event is identified by (rule, consumed elements) and the causal network by its identity-labelled edges. Networks from different orders are compared first for identity and then, if they differ, up to isomorphism by brute force over event permutations. A supplementary (not pre-registered) run covers all 127 non-overlapping systems with lhs length up to 4 (which includes genuinely non-overlapping pairs such as {AAB, BBBA} and {AABB, BBAA}) from all 126 initial strings of length 1-6. Run time about 3 s.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 1 fraction of non-overlapping (rule set, initial string) pairs with >= 2 complete evolutions whose causal networks all coincide (n = 186, exact (exhaustive within the family)). Interpretation: Wolfram's generalized substitution systems (NKS pp. 497-503) replace one occurrence of a left-hand block at a time; which occurrence, and when, is the free choice of 'order'. A causal network has one node per replacement event and an edge from event P to event E whenever E's matched block contains an element that P produced; the initial condition is represented by a node 0 that 'produces' the initial elements. Two orders give 'the same causal network' if the networks are isomorphic as node-labelled directed graphs (labels = rule applied, node 0 fixed). Non-overlap is the syntactic condition of p. 503: no non-empty proper suffix of any block equals a prefix of any block (including the block itself), and no block is a substring of another. To compare complete histories across orders, the enumeration is restricted to systems whose every rule strictly shortens the string (|rhs| < |lhs|), so every evolution terminates after finitely many events; all complete evolutions (all choices at every step) from every initial string of length <= 5 over {A, B} are generated exhaustively. Wolfram's weaker condition (no overlap among strings actually generated) is not tested.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch09-17: supports, confidence 0.93";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-17/result.json>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1>;
<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: shrinking-substitution-systems-2-letters-exhaustive";
<https://w3id.org/delphi/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<https://w3id.org/delphi/ontology/disconfirmingObservation> "Pre-registered: at least one non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "The enumeration is restricted to terminating (strictly shrinking) systems so that complete histories can be compared; for non-terminating systems the statement concerns infinite causal networks and was not tested. Within the family the result is exhaustive: all 186 (primary) and 524 (supplementary) non-overlapping cases with a genuine choice of order gave identical, not merely isomorphic, causal networks and identical final strings, while 96.6% of overlapping rule sets showed order-dependent networks for some initial string, so the non-overlap condition is doing real work.",
"Within the pre-registered family (lhs length <= 3) every non-overlapping rule set has a single multi-letter block or only single-letter blocks; non-overlapping pairs of multi-letter blocks appear only in the supplementary run with blocks of length 4, which was added after the primary run and is reported separately.",
"Wolfram's weaker condition (no overlaps among the strings actually generated) and his extension to network rewriting systems were not tested; the causal-network definition (edge from the event that produced an element to the event that consumes it, with an 'init' node for the initial condition) follows pp. 497-503 but the book gives it only pictorially.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered: among all enumerated (rule set, initial string) pairs whose rule set is syntactically non-overlapping and which admit at least two distinct complete evolutions, 100% have exactly one causal-network isomorphism class (and one final string) over all complete evolutions; and at least 10% of the overlapping rule sets exhibit at least two non-isomorphic causal networks for some initial string (otherwise the test has no discriminating power and the verdict is 'inconclusive', reason 'not-operationalizable').";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered: at least one non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.93"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "For every string substitution system whose left-hand-side blocks can never overlap themselves or each other, every possible order of performing replacements from a given initial string yields the same causal network (up to isomorphism), whereas systems with overlapping blocks can yield different causal networks for different orders.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py enumerates all 2305 one- and two-rule systems over {A,B} with lhs length 1-3 and strictly shorter rhs, classifies each syntactically as non-overlapping (37 systems; lhs sets {A}, {B}, {A,B}, {AB}, {BA}, {AAB}, {ABB}, {BAA}, {BBA}) or overlapping (2268), and for each of the 62 initial strings of length 1-5 generates every complete evolution by depth-first search over all possible replacement choices, tracking element identities so that each event is identified by (rule, consumed elements) and the causal network by its identity-labelled edges. Networks from different orders are compared first for identity and then, if they differ, up to isomorphism by brute force over event permutations. A supplementary (not pre-registered) run covers all 127 non-overlapping systems with lhs length up to 4 (which includes genuinely non-overlapping pairs such as {AAB, BBBA} and {AABB, BBAA}) from all 126 initial strings of length 1-6. Run time about 3 s.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered: among all enumerated (rule set, initial string) pairs whose rule set is syntactically non-overlapping and which admit at least two distinct complete evolutions, 100% have exactly one causal-network isomorphism class (and one final string) over all complete evolutions; and at least 10% of the overlapping rule sets exhibit at least two non-isomorphic causal networks for some initial string (otherwise the test has no discriminating power and the verdict is 'inconclusive', reason 'not-operationalizable').";
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dc:description "exhaustive finite family; non-overlapping systems are the test set, overlapping ones the control";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All one- and two-rule string substitution systems over {A,B} with left-hand blocks of length 1-3 and strictly shorter right-hand sides, all initial strings of length 1-5, all complete evolutions (generated by analysis.py)" .
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