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| It is aimed to be as the final version for the official HeKatE project (grant). | It is aimed to be as the final version for the official HeKatE project (grant). | ||
| + | //Please put bigger remarks/discussusion, to the [[hekatedev:xtt2|XTT2 development page]]// | ||
| ===== Introduction ===== | ===== Introduction ===== | ||
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| In contrast to traditional rulebases design approaches allowing for a //flat// (single-level) set of rules (e.g. using the Rete-based inference engines) XTT introduces an explicit //structure// in the rulebase, by introducing: | In contrast to traditional rulebases design approaches allowing for a //flat// (single-level) set of rules (e.g. using the Rete-based inference engines) XTT introduces an explicit //structure// in the rulebase, by introducing: | ||
| - | * //tables//, used to represent groups of rules working in the same context and hence having similar structure of preconditions, | + | * //tables//, used to represent groups of rules working in the same context (having similar structure of preconditions), |
| * //intertable links//, used to provide explicit specification of inference control, namely switching between tables, that allow for decision-tree like structure. | * //intertable links//, used to provide explicit specification of inference control, namely switching between tables, that allow for decision-tree like structure. | ||
| Line 29: | Line 29: | ||
| XTT is a formal method based on an expressive logical calculus called //Attributive Logic// (or //Attribute Logic//). | XTT is a formal method based on an expressive logical calculus called //Attributive Logic// (or //Attribute Logic//). | ||
| - | |||
| ==== History and Related Documents ==== | ==== History and Related Documents ==== | ||
| FIXME | FIXME | ||
| Line 67: | Line 66: | ||
| However, in the future the ARD+ shall be replaced by more advanced methods. | However, in the future the ARD+ shall be replaced by more advanced methods. | ||
| - | Basing on the above experiences, the current version of XTT known as XTT^2 has been proposed for the HeKatE project by Grzegorz J. Nalepa and Antoni Ligęza in 2008. | + | Based on the above experiences, the current version of XTT known as XTT^2 has been proposed for the HeKatE project by Grzegorz J. Nalepa and Antoni Ligęza in 2008. |
| XTT^2 uses ALSV(FD) (//Attributive Logic with Set Variables over Finite Domains//) as the formal foundation. | XTT^2 uses ALSV(FD) (//Attributive Logic with Set Variables over Finite Domains//) as the formal foundation. | ||
| Line 101: | Line 100: | ||
| ==== XTT Constraints ==== | ==== XTT Constraints ==== | ||
| - | Rule prototypes these hint for XTT tables: | + | Rule prototypes provide hints for XTT tables: |
| * structure -> what attributes are in the condidtion and conclusion | * structure -> what attributes are in the condidtion and conclusion | ||
| * state changes in conclusion -> in the value modification only attributes present in the given table may be used | * state changes in conclusion -> in the value modification only attributes present in the given table may be used | ||
| Line 167: | Line 166: | ||
| See [[hekate:xtt2#Inference]] for more details. | See [[hekate:xtt2#Inference]] for more details. | ||
| - | |||
| ==== Rule RHS ==== | ==== Rule RHS ==== | ||
| Line 177: | Line 175: | ||
| The rule RHS can contain: | The rule RHS can contain: | ||
| - | * state changes, that is attribute values modifications (with use of retract/assert), | + | * state changes, that is attribute values modifications (with use of retract/assert, FIXME by iw: there is no assert/retract anymore, assuming that attributes can be multivalued, there are only set operations, an assert is represented as a sum: assert(A(1)) <=> A = A u {1}), possibly with use of any predefined predicates/functions etc. for now we assume all the results are explicitly represented in state! |
| * external actions execution, that do not change attribute values, thus do not change the system state; these include output values definition and export, | * external actions execution, that do not change attribute values, thus do not change the system state; these include output values definition and export, | ||
| * link that specifies inference control (e.g. a switch/case or a loop), | * link that specifies inference control (e.g. a switch/case or a loop), | ||
| - | * execution of any well-defined procedure for calculation of a function defined for input attribute values FIXME (//chain calculations, loop/iterative calculations, transactions, control parameter calculations//; problem of bactracking! Do we have to put all the values to the state???). | + | |
| + | ++++Some consequences - backtracking| | ||
| + | no parameter passing, | ||
| + | no backtracking, | ||
| + | simple solution | ||
| + | ++++ | ||
| === Attribute value modification === | === Attribute value modification === | ||
| Line 200: | Line 203: | ||
| - | 2.2) Algebraic expressions in case of numeric attributes only; the expression can contain numbers, predefined algebraic operators and functions, as well as attribute values (Prolog //is//). | + | 2.2) Algebraic expressions in case of numeric attributes only; the expression can contain numbers, predefined algebraic operators and functions/predicates, as well as attribute values (Prolog //is//). |
| 3) External action specification; | 3) External action specification; | ||
| Line 231: | Line 234: | ||
| A table provides a //visual// representation of rules, as below. | A table provides a //visual// representation of rules, as below. | ||
| - | {{xttp-table-new.png|XTT table new format}} | + | {{xttp-table-new.png|XTT table new format}} FIXME |
| Rules in the table are interpreted one by one in a given way (see [[hekate:xtt2#Inference]]), this is the Table Inference. | Rules in the table are interpreted one by one in a given way (see [[hekate:xtt2#Inference]]), this is the Table Inference. | ||
| Line 237: | Line 240: | ||
| Table rows (rules) may be connected to other tables (rows) by links. | Table rows (rules) may be connected to other tables (rows) by links. | ||
| This forms a tree-like structure. | This forms a tree-like structure. | ||
| - | This is the Tree Inference. FIXME (//In fact, it is more close to a **graph** representing a partial order of inference//). | + | This is the Tree-like Inference. |
| + | (//In fact, it is more close to a **graph** representing a partial order of inference//). | ||
| ==== Table Scheme ==== | ==== Table Scheme ==== | ||
| Line 333: | Line 337: | ||
| * //rule-rule// (r2r) a given rule in a given table when fired, transfers control to another rule in another table, or possibly //the same table// (inside table link. | * //rule-rule// (r2r) a given rule in a given table when fired, transfers control to another rule in another table, or possibly //the same table// (inside table link. | ||
| - | **** More on intertable links| | + | FIXME: iw: I'm still not convinced about rule-rule links, any advantages? There are some disadvantages though, ie: if we change the rule firing order (let's say bottom-up instead of top-down,) rule-rule links can screw us really bad. Having rule-table links only forces designer to come up with well designed conditions. So, because there are some doubts I would recommend not implementing it for time being at all. |
| + | |||
| + | ++++More on intertable links| | ||
| In general, we should have inter-tables links and inside-table links. | In general, we should have inter-tables links and inside-table links. | ||
| Both of them can be defined with TableOut.RuleOut --> TableIN.RuleIN model. | Both of them can be defined with TableOut.RuleOut --> TableIN.RuleIN model. | ||
| However, for the inside table links we can define simple policies, such as a top-bottom order, top-first-fired order, without without circular interpretation. | However, for the inside table links we can define simple policies, such as a top-bottom order, top-first-fired order, without without circular interpretation. | ||
| - | **** | + | ++++ |
| === Link implementation === | === Link implementation === | ||
| Line 348: | Line 354: | ||
| Problem: In a general case, there might be multiple entry points in the XTT structure. | Problem: In a general case, there might be multiple entry points in the XTT structure. | ||
| - | Consider a tree (Ts are XTT tables) structure like this: | + | (See the discussion at the [[hekatedev:xtt2#Branching]] page.) |
| - | T1- | + | |
| - | > T5 - | + | |
| - | T2- \ | + | |
| - | T7 | + | |
| - | T3- / | + | |
| - | > T6 - | + | |
| - | T4- | + | |
| - | + | ||
| - | A //fired table// is a table already interpreted by the engine. | + | |
| - | + | ||
| - | To handle this we might introduce a simple backward-chaining approach. | + | |
| - | * build a list of tables that can be fired | + | |
| - | * fire any table with no preceding table, no incoming links or mark a selected table as a start table, | + | |
| - | * follow links to fire subsequent tables | + | |
| - | * to fire a table, no attributes in the condition can have the //NOT_DEFINED// value, in case of such a table backtrack to another table preceding this one | + | |
| - | * another solution, suitable for a single pass interpreter is to keep track of fired tables. | + | |
| - | + | ||
| - | Another approach would be to predetermine the sets of tables can be fired at the beginning of the inference by a backward-chaining analysis of table schemes (ARD prototypes). | + | |
| - | + | ||
| - | The above problem seem to apply only to the initial inference, not to a general branching structure like this: | + | |
| - | Tj | + | |
| - | / \ | + | |
| - | Ti Tl | + | |
| - | \ / | + | |
| - | Tk | + | |
| - | In this case the inference is deterministic, and depends on which rules in the first table Ti are fired. | + | |
| - | + | ||
| - | FIXME ALi | + | |
| - | The problem is that when admitting parallel operation it immediately becomes INDETERMINISTIC!!! | + | |
| - | + | ||
| - | Depending on the order, different results can be produced. And we cannot follow and examine all the orders. | + | |
| - | + | ||
| - | Moreover, various problems, such as deadlock, can occur. | + | |
| - | + | ||
| - | The quick solution is to establish a linear order of inference. | + | |
| - | + | ||
| - | A partial order (i.e. what we have) should be satisfactory, under the assumption that tables are independent. This can be checked by verifying that output (modified) attributes of a certain table do not come as inputs of another one to be executed in parallel. In fact, we must exmone all such CHAINS of DEPENDENCIES for safety. Perhaps ARD can be helpful? E.g. detecting loops at the level of ARD would be easier. | + | |
| - | A general idea is that we can implement and ARD-Analyzer for detecting possible problems (dependent attributes in parallel chains) and insist on explicite order definition (even at the level of ARD). | + | //A temporary semi-parallel solution//: |
| + | ARD introduces partial order in tables, | ||
| + | tables can be fired in any way, | ||
| + | as long as this contstraint holds. | ||
| - | (Please discuss at the [[hekatedev:xtt2#Branching]] page.) | + | FIXME: iw: not really there might be more than one table with input attributes (or ro, rw) in the condition parts, it might be not doable to infer which table should be run first. |
| + | There might be an algorithm implemented which finds an order of execution (which table to start with), but any conditions using a N/D value can screw it. | ||
| + | I'd suggest choosing an entry table, the one that the inference process starts with, explicitly. | ||
| ==== Interpreter Scenarios ==== | ==== Interpreter Scenarios ==== | ||
| Line 477: | Line 451: | ||
| * communication (comm) (S <-> E) | * communication (comm) (S <-> E) | ||
| Arrows indicate the System/Environment interaction. | Arrows indicate the System/Environment interaction. | ||
| + | |||
| + | FIXME: iw: what's happened to ''ro, rw, wo, state'' classes? | ||
| Discuss ideas here: [[hekatedev:xtt2#Attribute Classes]]. | Discuss ideas here: [[hekatedev:xtt2#Attribute Classes]]. | ||
| Line 489: | Line 465: | ||
| ===== HeKatE Meta Representation ===== | ===== HeKatE Meta Representation ===== | ||
| - | |||
| - | FIXME ALi | ||
| The following textual algebraic representation is provided. | The following textual algebraic representation is provided. | ||
| Line 508: | Line 482: | ||
| Fact: | Fact: | ||
| - | FIXME ALi | + | |
| - | Here - sorry; I am not sure about the idea -- do not understand. Explanations necessary. | + | |
| ===== XTT Analysis ===== | ===== XTT Analysis ===== | ||
