489:, describes (in its first rule) that E. coli can feed on the sugar lactose if it makes two enzymes permease and galactosidase. Like all enzymes, these are made if they are coded by a gene (Gene) that is expressed (described by the second rule). The two enzymes of permease and galactosidase are coded by two genes, lac(y) and lac(z) respectively (stated in the fifth and sixth rule of the program), in a cluster of genes (lac(X)) – called an operon – that is expressed when the amounts (amt) of glucose are low and lactose are high or when they are both at medium level (see the fourth and fifth rule). The abducibles,
1785:
extensions always have a unique model. Many of the ALP systems use the entailment view of the integrity constraints as this can be easily implemented without the need for any extra specialized procedures for the satisfaction of the integrity constraints since this view treats the constraints in the same way as the problem goal. In many practical cases, the third condition in this formal definition of an abductive explanation in ALP is either trivially satisfied or it is contained in the second condition via the use of specific integrity constraints that capture consistency.
36:
249:
IC. The extension or completion of the problem description given by the abductive explanations provides new information, hitherto not contained in the solution to the problem. Quality criteria to prefer one solution over another, often expressed via integrity constraints, can be applied to select specific abductive explanations of the problem
987:
992:
The decision which of the two to adopt could depend on additional information that is available, e.g. it may be known that when the level of glucose is low then the organism exhibits a certain behaviour – in the model such additional information is that the temperature of the organism is low – and by
248:
and the integrity constraints IC both hold. Thus abductive explanations extend the logic program P by the addition of full or partial definitions of the abducible predicates. In this way, abductive explanations form solutions of the problem according to the description of the problem domain in P and
119:
by allowing some predicates to be incompletely defined, declared as abducible predicates. Problem solving is effected by deriving hypotheses on these abducible predicates (abductive hypotheses) as solutions of problems to be solved. These problems can be either observations that need to be explained
1784:
is consistent, can be sufficient, meaning that there exists at least one model (possible ensuing world) of the extended program where the integrity constraints hold. In practice, in many cases, these two ways of formalizing the role of the integrity constraints coincide as the logic program and its
473:
The goal "John is citizen" has two abductive solutions, one of which is "John is born in the USA", the other of which is "John is born outside the USA" and "John is registered". The potential solution of becoming a citizen by residence and naturalization fails because it violates the integrity
1693:
and the notion of consistency of the (extended) logic programs. Any of the different semantics of logic programming such as the completion, stable or well-founded semantics can (and have been used in practice) to give different notions of abductive explanations and thus different forms of ALP
225:
The clauses in P define a set of non-abducible predicates and through this they provide a description (or model) of the problem domain. The integrity constraints in IC specify general properties of the problem domain that need to be respected in any solution of a problem.
493:, declare all ground instances of the predicates "amount" as assumable. This reflects that in the model the amounts at any time of the various substances are unknown. This is incomplete information that is to be determined in each problem case. The integrity constraints,
1724:
as restrictions on the possible abductive solutions. It requires that these are entailed by the logic program extended with an abductive solution, thus meaning that in any model of the extended logic program (which one can think of as an ensuing world given
908:
408:
The observation that the grass is wet has two potential explanations, "it rained" and "the sprinkler was on", which entail the observation. However, only the second potential explanation, "the sprinkler was on", satisfies the integrity constraint.
233:, which expresses either an observation that needs to be explained or a goal that is desired, is represented by a conjunction of positive and negative (NAF) literals. Such problems are solved by computing "abductive explanations" of
256:
Computation in ALP combines the backwards reasoning of normal logic programming (to reduce problems to sub-problems) with a kind of integrity checking to show that the abductive explanations satisfy the integrity constraints.
206:
Normally, the logic program P does not contain any clauses whose head (or conclusion) refers to an abducible predicate. (This restriction can be made without loss of generality.) Also in practice, many times, the
996:
Once an explanation has been chosen, then this becomes part of the theory, which can be used to draw new conclusions. The explanation and more generally these new conclusions form the solution of the problem.
2325:
260:
The following two examples, written in simple structured
English rather than in the strict syntax of ALP, illustrate the notion of abductive explanation in ALP and its relation to problem solving.
1526:
311:
1782:
463:
together with the five abducible predicates, "is born in the USA", "is born outside the USA", "is a resident of the USA", "is naturalized" and "is registered" and the integrity constraint:
1016:
Consider the classic example of reasoning by default that a bird can fly if it cannot be shown that the bird is abnormal. Here is a variant of the example using negation as failure:
982:{\displaystyle {\begin{cases}\Delta _{1}=\{{\text{amount(lactose, hi), amount(glucose, low)}}\}\\\Delta _{2}=\{{\text{amount(lactose, medium), amount(glucose, medium)}}\}\end{cases}}}
900:
1637:
186:
2231:
1601:
2295:
1722:
396:
1664:
2244:
65:
1691:
1743:
1566:
244:
is a set of positive (and sometimes also negative) ground instances of the abducible predicates, such that, when these are added to the logic program P, the problem
1844:
Poole, David; Goebel, Randy; Aleliunas, Romas (1987). "Theorist: A Logical
Reasoning System for Defaults and Diagnosis". In Nick J. Cercone; Gordon McCalla (eds.).
1793:
Most of the implementations of ALP extend the SLD resolution-based computational model of logic programming. ALP can also be implemented by means of its link with
1318:. The conclusion can be derived from the assumption because it cannot be shown that the integrity constraint is violated, which is because it cannot be shown that
2394:
2329:
1546:
369:
331:
1745:) the requirements of the integrity constraints are met. In some cases this may be unnecessarily strong and the weaker requirement of consistency, namely that
902:. This can arise either as an observation to be explained or as a state of affairs to be achieved by finding a plan. This goal has two abductive explanations:
1673:
This definition leaves open the choice of the underlying semantics of logic programming through which we give the exact meaning of the entailment relation
2224:
2458:
2808:
2670:
1797:(ASP), where the ASP systems can be employed. Examples of systems of the former approach are ACLP, A-system, CIFF, SCIFF, ABDUAL and ProLogICA.
2814:
2140:
2217:
2099:
1925:
1861:
2999:
2747:
2467:
1944:
2118:
87:
2839:
2519:
2463:
1956:
217:
Such a constraint means that it is not possible for all A1,...,An to be true and at the same time all of B1,...,Bm to be false.
2699:
2572:
2503:
2438:
2361:
2877:
2640:
2270:
485:
The abductive logic program below describes a simple model of the lactose metabolism of the bacterium E. coli. The program,
2655:
2645:
2423:
3039:
3019:
2949:
2892:
2854:
2844:
2804:
2729:
2665:
2635:
2562:
2551:
2448:
2428:
2403:
2366:
2028:
1486:
271:
1884:
Eshghi, K. and
Kowalski, R.A., 1989, June. Abduction Compared with Negation by Failure. In ICLP (Vol. 89, pp. 234-255).
48:
2994:
2757:
2724:
2619:
2595:
2557:
2433:
2342:
2320:
2305:
1806:
1748:
58:
52:
44:
3060:
2941:
2927:
2834:
2794:
2719:
2625:
2605:
2472:
2351:
2285:
1935:
Kakas, A.C.; Mancarella, P. (1990). "Generalised Stable Models: A Semantics for
Abduction". In Aiello, L.C. (ed.).
1480:
The formal semantics of the central notion of an abductive explanation in ALP can be defined in the following way.
2026:
Denecker, Marc; De
Schreye, Danny (February 1998). "SLDNFA: An Abductive Procedure for Abductive Logic Programs".
1378:
violates the integrity constraint. This manner of reasoning in ALP simulates reasoning with negation as failure.
3034:
2799:
2709:
2689:
2675:
69:
3014:
2974:
2917:
2849:
2587:
2418:
108:
993:
observing the truth or falsity of this it is possible to choose the first or second explanation respectively.
877:
1607:
147:
3024:
3004:
2945:
2932:
2912:
2739:
2476:
2380:
2338:
1574:
1697:
The above definition takes a particular view on the formalization of the role of the integrity constraints
2984:
2959:
2953:
2897:
2859:
2547:
2542:
2494:
2389:
2290:
2262:
2253:
2037:
2004:
1965:
1794:
1465:
1382:
2886:
2882:
2824:
2776:
2346:
208:
3029:
3009:
2969:
2771:
2630:
2499:
2486:
2240:
1954:
Console, L.; Dupre, D.T.; Torasso, P. (1991). "On the
Relationship between Abduction and Deduction".
2171:
1700:
917:
374:
2964:
2902:
2714:
2694:
2680:
2412:
2280:
2275:
2042:
2009:
1970:
1643:
1010:
133:
112:
2781:
2734:
2704:
2650:
2509:
2408:
2300:
2209:
2163:
1867:
477:
A more complex example that is also written in the more formal syntax of ALP is the following.
2937:
2829:
2684:
2660:
2600:
2567:
2529:
2514:
2453:
2095:
2087:
1940:
1921:
1913:
1857:
1676:
1006:
199:
121:
116:
1728:
1551:
2819:
2751:
2615:
2356:
2155:
2127:
2072:
2047:
2014:
1975:
1849:
1827:
129:
1381:
Conversely, it is possible to simulate abduction in ALP using negation as failure with the
17:
2869:
2743:
2609:
2310:
1988:
2092:
Computational Logic: Logic
Programming and Beyond: Essays in Honour of Robert A. Kowalski
1897:, 1992. Abductive logic programming. Journal of logic and computation, 2(6), pp.719-770.
2921:
2577:
2443:
1992:
1894:
1531:
417:
Consider the abductive logic program consisting of the following (simplified) clauses:
354:
316:
2204:
2077:
2060:
2051:
3054:
2907:
2141:"Inference of abduction theories for handling incompleteness in first-order learning"
2131:
2167:
1871:
2110:
2094:. Lecture Notes in Computer Science. Vol. 2407. Springer. pp. 402–437.
1848:. Symbolic Computation (1st ed.). New York, NY: Springer. pp. 331–352.
2789:
371:
are "it rained" and "the sprinkler was on" and the only integrity constraint in
2159:
1937:
ECAI 90: proceedings of the 9th
European Conference on Artificial Intelligence
1853:
1667:
2194:
2018:
1979:
211:
in IC are often restricted to the form of denials, i.e. clauses of the form:
2139:
Esposito, F.; Ferilli, S.; Basile, T.M.A.; Di Mauro, N. (February 2007).
125:
1846:
The
Knowledge Frontier – Essays in the Representation of Knowledge
1464:
is true. This technique for simulating abduction is commonly used in
497:, state that the amount of any substance (S) can only take one value.
192:
P is a logic program of exactly the same form as in logic programming
111:
framework that can be used to solve problems declaratively, based on
2199:
120:(as in classical abduction) or goals to be achieved (as in normal
1918:
The
Knowledge Frontier: Essays in the Representation of Knowledge
1914:"Theorist: a logical reasoning system for defaults and diagnosis"
2189:
1005:
As shown in the Theorist system, abduction can also be used for
2213:
1828:
Theorist: A Logical Reasoning System for Defaults and Diagnosis
195:
A is a set of predicate names, called the abducible predicates
29:
1763:
1760:
1709:
1706:
1510:
1507:
1385:. This can be done by adding, for every abducible predicate
383:
380:
295:
292:
975:
1826:
Poole, David; Goebel, Randy; Aleliunas, Romas (Feb 1986).
1446:
This pair of clauses has two stable models, one in which
1128:
Here is the same example using an abducible predicate
1751:
1731:
1703:
1679:
1646:
1610:
1577:
1554:
1534:
1489:
911:
880:
377:
357:
319:
274:
150:
2111:"Probabilistic Horn abduction and Bayesian networks"
2983:
2868:
2770:
2586:
2528:
2485:
2388:
2379:
2319:
2261:
2252:
1568:of ground atoms on abducible predicates such that:
1456:
1447:
1395:
1386:
1364:
1349:
1334:
1319:
1304:
1289:
1271:
1256:
1129:
1776:
1737:
1716:
1685:
1658:
1631:
1595:
1560:
1540:
1521:{\displaystyle \langle P,A,{\mathit {IC}}\rangle }
1520:
1288:Using abduction in ALP it is possible to conclude
981:
894:
390:
363:
325:
306:{\displaystyle \langle P,A,{\mathit {IC}}\rangle }
305:
180:
124:). It can be used to solve problems in diagnosis,
1777:{\displaystyle P\cup {\mathit {IC}}\cup \Delta }
966:amount(lactose, medium), amount(glucose, medium)
144:Abductive logic programs have three components,
57:but its sources remain unclear because it lacks
2225:
1912:Poole, D.; Goebel, R.; Aleliunas, R. (1987).
8:
2061:"Special issue: abductive logic programming"
1916:. In Cercone, Nick; McCalla, Gordon (eds.).
1515:
1490:
1333:In contrast, it is not possible to conclude
969:
961:
941:
933:
300:
275:
172:
151:
1009:. Moreover, abduction in ALP can simulate
27:Logic programming using abductive reasoning
2385:
2258:
2232:
2218:
2210:
2296:Programming in the large and in the small
2076:
2041:
2008:
1969:
1759:
1758:
1750:
1730:
1705:
1704:
1702:
1678:
1645:
1609:
1576:
1553:
1533:
1528:, an abductive explanation for a problem
1506:
1505:
1488:
964:
952:
938:amount(lactose, hi), amount(glucose, low)
936:
924:
912:
910:
887:
879:
379:
378:
376:
356:
318:
291:
290:
273:
149:
88:Learn how and when to remove this message
895:{\displaystyle G={\text{feed(lactose)}}}
214:false:- A1,...,An, not B1, ..., not Bm.
2059:Denecker, M.; Kakas, A.C. (July 2000).
1995:(1993). "Abductive Logic Programming".
1818:
1632:{\displaystyle P\cup \Delta \models IC}
181:{\displaystyle \langle P,A,IC\rangle ,}
1596:{\displaystyle P\cup \Delta \models G}
240:An abductive explanation of a problem
1143:with an integrity constraint in ALP:
132:. It has also been used to interpret
7:
2090:. In Kakas, A.C.; Sadri, F. (eds.).
221:Informal meaning and problem solving
405:it rained and the sun was shining.
2086:Denecker, M.; Kakas, A.C. (2002).
1833:(Research Report). Univ. Waterloo.
1771:
1732:
1653:
1617:
1584:
1555:
1483:Given an abductive logic program,
949:
921:
136:as a form of abductive reasoning.
25:
2148:Knowledge and Information Systems
1394:an additional contrary predicate
1270:is the contrary of the predicate
2840:Partitioned global address space
2088:"Abduction in Logic Programming"
1997:Journal of Logic and Computation
1957:Journal of Logic and Computation
1893:Kakas, A.C., Kowalski, R.A. and
1455:is true, and the other in which
34:
470:John is a resident of the USA.
1920:. Springer. pp. 331–352.
1717:{\displaystyle {\mathit {IC}}}
391:{\displaystyle {\mathit {IC}}}
200:first-order classical formulae
1:
2078:10.1016/S0743-1066(99)00078-3
2052:10.1016/S0743-1066(97)00074-5
1659:{\displaystyle P\cup \Delta }
1013:in normal logic programming.
268:The abductive logic program,
2367:Uniform Function Call Syntax
2132:10.1016/0004-3702(93)90061-F
2065:Journal of Logic Programming
2029:Journal of Logic Programming
1939:. Pitman. pp. 385–391.
351:The abducible predicates in
2835:Parallel programming models
2809:Concurrent constraint logic
1807:Inductive logic programming
458:Mary is the mother of John.
434:X is a resident of the USA
101:Abductive logic programming
18:Abductive Logic Programming
3077:
2928:Metalinguistic abstraction
2795:Automatic mutual exclusion
1789:Implementation and systems
1468:to solve problems using a
789:Integrity constraints (IC)
444:X is born outside the USA
430:X is born outside the USA
2800:Choreographic programming
2160:10.1007/s10115-006-0019-5
1854:10.1007/978-1-4612-4792-0
333:the following sentences:
2850:Relativistic programming
1686:{\displaystyle \models }
1405:
1255:The abducible predicate
1145:
1018:
1001:Default reasoning in ALP
855:
792:
504:
109:knowledge-representation
43:This article includes a
2119:Artificial Intelligence
1738:{\displaystyle \Delta }
1561:{\displaystyle \Delta }
1403:and a pair of clauses:
1363:together with the fact
1348:because the assumption
128:, natural language and
72:more precise citations.
2860:Structured concurrency
2245:Comparison by language
2019:10.1093/logcom/2.6.719
1980:10.1093/logcom/1.5.661
1795:Answer Set Programming
1778:
1739:
1718:
1687:
1660:
1633:
1597:
1562:
1542:
1522:
1466:answer set programming
1383:stable model semantics
983:
896:
392:
365:
327:
307:
182:
2825:Multitier programming
2641:Interface description
2241:Programming paradigms
1779:
1740:
1719:
1688:
1661:
1634:
1598:
1563:
1543:
1523:
1303:under the assumption
984:
897:
448:Y is the mother of X
424:X is born in the USA.
393:
366:
348:The sun was shining.
346:the sprinkler was on.
328:
308:
209:integrity constraints
183:
1749:
1729:
1701:
1677:
1644:
1608:
1575:
1552:
1532:
1487:
1273:abnormal_flying_bird
1066:abnormal_flying_bird
1054:abnormal_flying_bird
909:
878:
874:The problem goal is
501:Domain knowledge (P)
375:
355:
317:
272:
148:
115:. It extends normal
2965:Self-modifying code
2573:Probabilistic logic
2504:Functional reactive
2459:Expression-oriented
2413:Partial application
1011:negation as failure
858:abducible_predicate
460:Mary is a citizen.
134:negation as failure
113:abductive reasoning
2878:Attribute-oriented
2651:List comprehension
2596:Algebraic modeling
2409:Anonymous function
2301:Design by contract
2271:Jackson structures
2109:Poole, D. (1993).
1774:
1735:
1714:
1683:
1656:
1629:
1593:
1558:
1538:
1518:
1351:normal_flying_bird
1306:normal_flying_bird
1258:normal_flying_bird
1193:normal_flying_bird
1175:normal_flying_bird
1131:normal_flying_bird
979:
974:
892:
388:
361:
323:
303:
178:
107:) is a high-level
45:list of references
3061:Logic programming
3048:
3047:
2938:Program synthesis
2830:Organic computing
2766:
2765:
2671:Non-English-based
2646:Language-oriented
2424:Purely functional
2375:
2374:
2101:978-3-540-43959-2
1927:978-0-387-96557-4
1863:978-1-4612-9158-9
1541:{\displaystyle G}
1470:generate and test
1007:default reasoning
967:
939:
890:
438:X is naturalized.
364:{\displaystyle A}
326:{\displaystyle P}
122:logic programming
117:logic programming
98:
97:
90:
16:(Redirected from
3068:
2950:by demonstration
2855:Service-oriented
2845:Process-oriented
2820:Macroprogramming
2805:Concurrent logic
2676:Page description
2666:Natural language
2636:Grammar-oriented
2563:Nondeterministic
2552:Constraint logic
2454:Point-free style
2449:Functional logic
2386:
2357:Immutable object
2276:Block-structured
2259:
2234:
2227:
2220:
2211:
2178:
2176:
2170:. Archived from
2145:
2135:
2115:
2105:
2082:
2080:
2055:
2045:
2022:
2012:
1983:
1973:
1950:
1931:
1898:
1891:
1885:
1882:
1876:
1875:
1841:
1835:
1834:
1832:
1823:
1783:
1781:
1780:
1775:
1767:
1766:
1744:
1742:
1741:
1736:
1723:
1721:
1720:
1715:
1713:
1712:
1692:
1690:
1689:
1684:
1665:
1663:
1662:
1657:
1638:
1636:
1635:
1630:
1602:
1600:
1599:
1594:
1567:
1565:
1564:
1559:
1547:
1545:
1544:
1539:
1527:
1525:
1524:
1519:
1514:
1513:
1476:Formal semantics
1463:
1462:
1459:
1454:
1453:
1450:
1442:
1439:
1436:
1433:
1430:
1427:
1424:
1421:
1418:
1415:
1412:
1409:
1402:
1401:
1398:
1393:
1392:
1389:
1377:
1376:
1373:
1370:
1367:
1362:
1361:
1358:
1355:
1352:
1347:
1346:
1343:
1340:
1337:
1332:
1331:
1328:
1325:
1322:
1317:
1316:
1313:
1310:
1307:
1302:
1301:
1298:
1295:
1292:
1284:
1283:
1280:
1277:
1274:
1269:
1268:
1265:
1262:
1259:
1251:
1248:
1245:
1242:
1239:
1236:
1233:
1230:
1227:
1224:
1221:
1218:
1215:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1185:
1182:
1179:
1176:
1173:
1170:
1167:
1164:
1161:
1158:
1155:
1152:
1149:
1142:
1141:
1138:
1135:
1132:
1124:
1121:
1118:
1115:
1112:
1109:
1106:
1103:
1100:
1097:
1094:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1055:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
988:
986:
985:
980:
978:
977:
968:
965:
957:
956:
940:
937:
929:
928:
901:
899:
898:
893:
891:
888:
868:
865:
862:
859:
847:
844:
841:
838:
835:
832:
829:
826:
823:
820:
817:
814:
811:
808:
805:
802:
799:
796:
784:
781:
778:
775:
772:
769:
766:
763:
760:
757:
754:
751:
748:
745:
742:
739:
736:
733:
730:
727:
724:
721:
718:
715:
712:
709:
706:
703:
700:
697:
694:
691:
688:
685:
682:
679:
676:
673:
670:
667:
664:
661:
658:
655:
652:
649:
646:
643:
640:
637:
634:
631:
628:
625:
622:
619:
616:
613:
610:
607:
604:
601:
598:
595:
592:
589:
586:
583:
580:
577:
574:
571:
568:
565:
562:
559:
556:
553:
550:
547:
544:
541:
538:
535:
532:
529:
526:
523:
520:
517:
514:
511:
508:
456:X is registered.
397:
395:
394:
389:
387:
386:
370:
368:
367:
362:
332:
330:
329:
324:
312:
310:
309:
304:
299:
298:
187:
185:
184:
179:
130:machine learning
93:
86:
82:
79:
73:
68:this article by
59:inline citations
38:
37:
30:
21:
3076:
3075:
3071:
3070:
3069:
3067:
3066:
3065:
3051:
3050:
3049:
3044:
2986:
2979:
2870:Metaprogramming
2864:
2780:
2775:
2762:
2744:Graph rewriting
2582:
2558:Inductive logic
2538:Abductive logic
2524:
2481:
2444:Dependent types
2392:
2371:
2343:Prototype-based
2323:
2321:Object-oriented
2315:
2311:Nested function
2306:Invariant-based
2248:
2238:
2186:
2181:
2174:
2143:
2138:
2113:
2108:
2102:
2085:
2058:
2025:
1986:
1953:
1947:
1934:
1928:
1911:
1907:
1902:
1901:
1892:
1888:
1883:
1879:
1864:
1843:
1842:
1838:
1830:
1825:
1824:
1820:
1815:
1803:
1791:
1747:
1746:
1727:
1726:
1699:
1698:
1675:
1674:
1642:
1641:
1606:
1605:
1573:
1572:
1550:
1549:
1530:
1529:
1485:
1484:
1478:
1460:
1457:
1451:
1448:
1444:
1443:
1440:
1437:
1434:
1431:
1428:
1425:
1422:
1419:
1416:
1413:
1410:
1407:
1399:
1396:
1390:
1387:
1374:
1371:
1368:
1365:
1359:
1356:
1353:
1350:
1344:
1341:
1338:
1335:
1329:
1326:
1323:
1320:
1314:
1311:
1308:
1305:
1299:
1296:
1293:
1290:
1281:
1278:
1275:
1272:
1266:
1263:
1260:
1257:
1253:
1252:
1249:
1246:
1243:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1216:
1213:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1156:
1153:
1150:
1147:
1139:
1136:
1133:
1130:
1126:
1125:
1122:
1119:
1116:
1113:
1110:
1107:
1104:
1101:
1098:
1095:
1092:
1089:
1086:
1083:
1080:
1077:
1074:
1071:
1068:
1065:
1062:
1059:
1056:
1053:
1050:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1003:
973:
972:
948:
945:
944:
920:
913:
907:
906:
876:
875:
870:
869:
866:
863:
860:
857:
849:
848:
845:
842:
839:
836:
833:
830:
827:
824:
821:
818:
815:
812:
809:
806:
803:
800:
797:
794:
786:
785:
782:
779:
776:
773:
770:
767:
764:
761:
758:
755:
752:
749:
746:
743:
740:
737:
734:
731:
728:
725:
722:
719:
716:
713:
710:
707:
704:
701:
698:
695:
692:
689:
686:
683:
680:
677:
674:
671:
668:
665:
662:
659:
656:
653:
650:
647:
644:
641:
638:
635:
632:
629:
626:
623:
620:
617:
614:
611:
608:
605:
602:
599:
596:
593:
590:
587:
584:
581:
578:
575:
572:
569:
566:
563:
560:
557:
554:
551:
548:
545:
542:
539:
536:
533:
530:
527:
524:
521:
518:
515:
512:
509:
506:
483:
471:
461:
459:
457:
452:Y is a citizen
440:X is a citizen
439:
426:X is a citizen
425:
420:X is a citizen
415:
406:
373:
372:
353:
352:
349:
347:
341:
315:
314:
270:
269:
266:
223:
215:
198:IC is a set of
146:
145:
142:
94:
83:
77:
74:
63:
49:related reading
39:
35:
28:
23:
22:
15:
12:
11:
5:
3074:
3072:
3064:
3063:
3053:
3052:
3046:
3045:
3043:
3042:
3037:
3032:
3027:
3022:
3017:
3012:
3007:
3002:
2997:
2991:
2989:
2981:
2980:
2978:
2977:
2972:
2967:
2962:
2957:
2935:
2930:
2925:
2915:
2910:
2905:
2900:
2895:
2890:
2880:
2874:
2872:
2866:
2865:
2863:
2862:
2857:
2852:
2847:
2842:
2837:
2832:
2827:
2822:
2817:
2812:
2802:
2797:
2792:
2786:
2784:
2768:
2767:
2764:
2763:
2761:
2760:
2755:
2740:Transformation
2737:
2732:
2727:
2722:
2717:
2712:
2707:
2702:
2697:
2692:
2687:
2678:
2673:
2668:
2663:
2658:
2653:
2648:
2643:
2638:
2633:
2628:
2626:Differentiable
2623:
2613:
2606:Automata-based
2603:
2598:
2592:
2590:
2584:
2583:
2581:
2580:
2575:
2570:
2565:
2560:
2555:
2545:
2540:
2534:
2532:
2526:
2525:
2523:
2522:
2517:
2512:
2507:
2497:
2491:
2489:
2483:
2482:
2480:
2479:
2473:Function-level
2470:
2461:
2456:
2451:
2446:
2441:
2436:
2431:
2426:
2421:
2416:
2406:
2400:
2398:
2383:
2377:
2376:
2373:
2372:
2370:
2369:
2364:
2359:
2354:
2349:
2335:
2333:
2317:
2316:
2314:
2313:
2308:
2303:
2298:
2293:
2288:
2286:Non-structured
2283:
2278:
2273:
2267:
2265:
2256:
2250:
2249:
2239:
2237:
2236:
2229:
2222:
2214:
2208:
2207:
2202:
2197:
2192:
2185:
2184:External links
2182:
2180:
2179:
2177:on 2011-07-17.
2154:(2): 217–242.
2136:
2106:
2100:
2083:
2056:
2043:10.1.1.21.6503
2036:(2): 111–167.
2023:
2010:10.1.1.37.3655
2003:(6): 719–770.
1989:Kowalski, R.A.
1984:
1971:10.1.1.31.9982
1964:(5): 661–690.
1951:
1946:978-0273088226
1945:
1932:
1926:
1908:
1906:
1903:
1900:
1899:
1886:
1877:
1862:
1836:
1817:
1816:
1814:
1811:
1810:
1809:
1802:
1799:
1790:
1787:
1773:
1770:
1765:
1762:
1757:
1754:
1734:
1711:
1708:
1682:
1671:
1670:
1655:
1652:
1649:
1639:
1628:
1625:
1622:
1619:
1616:
1613:
1603:
1592:
1589:
1586:
1583:
1580:
1557:
1537:
1517:
1512:
1509:
1504:
1501:
1498:
1495:
1492:
1477:
1474:
1406:
1146:
1019:
1002:
999:
990:
989:
976:
971:
963:
960:
955:
951:
947:
946:
943:
935:
932:
927:
923:
919:
918:
916:
886:
883:
872:
871:
856:
853:
852:Abducibles (A)
850:
793:
790:
787:
505:
502:
482:
479:
465:
419:
414:
411:
400:
385:
382:
360:
335:
322:
302:
297:
294:
289:
286:
283:
280:
277:
265:
262:
222:
219:
213:
204:
203:
196:
193:
177:
174:
171:
168:
165:
162:
159:
156:
153:
141:
138:
96:
95:
53:external links
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3073:
3062:
3059:
3058:
3056:
3041:
3038:
3036:
3033:
3031:
3028:
3026:
3023:
3021:
3018:
3016:
3013:
3011:
3010:Data-oriented
3008:
3006:
3003:
3001:
2998:
2996:
2993:
2992:
2990:
2988:
2982:
2976:
2973:
2971:
2968:
2966:
2963:
2961:
2958:
2955:
2951:
2947:
2943:
2939:
2936:
2934:
2931:
2929:
2926:
2923:
2919:
2916:
2914:
2911:
2909:
2908:Homoiconicity
2906:
2904:
2901:
2899:
2896:
2894:
2891:
2888:
2884:
2881:
2879:
2876:
2875:
2873:
2871:
2867:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2815:Concurrent OO
2813:
2810:
2806:
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2787:
2785:
2783:
2778:
2773:
2769:
2759:
2756:
2753:
2749:
2745:
2741:
2738:
2736:
2733:
2731:
2728:
2726:
2723:
2721:
2718:
2716:
2713:
2711:
2710:Set-theoretic
2708:
2706:
2703:
2701:
2698:
2696:
2693:
2691:
2690:Probabilistic
2688:
2686:
2682:
2679:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2654:
2652:
2649:
2647:
2644:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2621:
2617:
2614:
2611:
2607:
2604:
2602:
2599:
2597:
2594:
2593:
2591:
2589:
2585:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2553:
2549:
2546:
2544:
2541:
2539:
2536:
2535:
2533:
2531:
2527:
2521:
2518:
2516:
2513:
2511:
2508:
2505:
2501:
2498:
2496:
2493:
2492:
2490:
2488:
2484:
2478:
2474:
2471:
2469:
2468:Concatenative
2465:
2462:
2460:
2457:
2455:
2452:
2450:
2447:
2445:
2442:
2440:
2437:
2435:
2432:
2430:
2427:
2425:
2422:
2420:
2417:
2414:
2410:
2407:
2405:
2402:
2401:
2399:
2396:
2391:
2387:
2384:
2382:
2378:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2344:
2340:
2337:
2336:
2334:
2331:
2327:
2322:
2318:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2268:
2266:
2264:
2260:
2257:
2255:
2251:
2246:
2242:
2235:
2230:
2228:
2223:
2221:
2216:
2215:
2212:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2187:
2183:
2173:
2169:
2165:
2161:
2157:
2153:
2149:
2142:
2137:
2133:
2129:
2126:(1): 81–129.
2125:
2121:
2120:
2112:
2107:
2103:
2097:
2093:
2089:
2084:
2079:
2074:
2070:
2066:
2062:
2057:
2053:
2049:
2044:
2039:
2035:
2031:
2030:
2024:
2020:
2016:
2011:
2006:
2002:
1998:
1994:
1990:
1987:Kakas, A.C.;
1985:
1981:
1977:
1972:
1967:
1963:
1959:
1958:
1952:
1948:
1942:
1938:
1933:
1929:
1923:
1919:
1915:
1910:
1909:
1904:
1896:
1890:
1887:
1881:
1878:
1873:
1869:
1865:
1859:
1855:
1851:
1847:
1840:
1837:
1829:
1822:
1819:
1812:
1808:
1805:
1804:
1800:
1798:
1796:
1788:
1786:
1768:
1755:
1752:
1695:
1680:
1669:
1650:
1647:
1640:
1626:
1623:
1620:
1614:
1611:
1604:
1590:
1587:
1581:
1578:
1571:
1570:
1569:
1535:
1502:
1499:
1496:
1493:
1481:
1475:
1473:
1472:methodology.
1471:
1467:
1404:
1384:
1379:
1286:
1144:
1017:
1014:
1012:
1008:
1000:
998:
994:
958:
953:
930:
925:
914:
905:
904:
903:
889:feed(lactose)
884:
881:
854:
851:
791:
788:
747:galactosidase
540:galactosidase
503:
500:
499:
498:
496:
492:
488:
480:
478:
475:
469:
464:
455:
451:
447:
443:
437:
433:
429:
423:
418:
412:
410:
404:
399:
358:
345:
342:Grass is wet
339:
336:Grass is wet
334:
320:
287:
284:
281:
278:
263:
261:
258:
254:
252:
247:
243:
238:
236:
232:
227:
220:
218:
212:
210:
201:
197:
194:
191:
190:
189:
175:
169:
166:
163:
160:
157:
154:
139:
137:
135:
131:
127:
123:
118:
114:
110:
106:
102:
92:
89:
81:
78:February 2015
71:
67:
61:
60:
54:
50:
46:
41:
32:
31:
19:
3015:Event-driven
2537:
2419:Higher-order
2347:Object-based
2172:the original
2151:
2147:
2123:
2117:
2091:
2071:(1–3): 1–4.
2068:
2064:
2033:
2027:
2000:
1996:
1961:
1955:
1936:
1917:
1889:
1880:
1845:
1839:
1821:
1792:
1696:
1694:frameworks.
1672:
1482:
1479:
1469:
1445:
1380:
1287:
1254:
1127:
1015:
1004:
995:
991:
873:
494:
490:
486:
484:
476:
474:constraint.
472:
467:
462:
453:
449:
445:
441:
435:
431:
427:
421:
416:
407:
402:
350:
343:
337:
267:
259:
255:
250:
245:
241:
239:
234:
230:
228:
224:
216:
205:
143:
104:
100:
99:
84:
75:
64:Please help
56:
3025:Intentional
3005:Data-driven
2987:of concerns
2946:Inferential
2933:Multi-stage
2913:Interactive
2790:Actor-based
2777:distributed
2720:Stack-based
2520:Synchronous
2477:Value-level
2464:Applicative
2381:Declarative
2339:Class-based
753:temperature
229:A problem,
70:introducing
3000:Components
2985:Separation
2960:Reflective
2954:by example
2898:Extensible
2772:Concurrent
2748:Production
2735:Templating
2715:Simulation
2700:Scientific
2620:Spacecraft
2548:Constraint
2543:Answer set
2495:Flow-based
2395:comparison
2390:Functional
2362:Persistent
2326:comparison
2291:Procedural
2263:Structured
2254:Imperative
1905:References
1668:consistent
340:it rained.
2887:Inductive
2883:Automatic
2705:Scripting
2404:Recursive
2038:CiteSeerX
2005:CiteSeerX
1966:CiteSeerX
1772:Δ
1769:∪
1756:∪
1733:Δ
1681:⊨
1654:Δ
1651:∪
1621:⊨
1618:Δ
1615:∪
1588:⊨
1585:Δ
1582:∪
1556:Δ
1548:is a set
1516:⟩
1491:⟨
950:Δ
922:Δ
481:Example 3
413:Example 2
313:, has in
301:⟩
276:⟨
264:Example 1
173:⟩
152:⟨
3055:Category
3040:Subjects
3030:Literate
3020:Features
2975:Template
2970:Symbolic
2942:Bayesian
2922:Hygienic
2782:parallel
2661:Modeling
2656:Low-code
2631:End-user
2568:Ontology
2500:Reactive
2487:Dataflow
2168:10699982
1993:Toni, F.
1895:Toni, F.
1872:38209923
1801:See also
723:permease
528:permease
126:planning
2995:Aspects
2903:Generic
2893:Dynamic
2752:Pattern
2730:Tactile
2695:Quantum
2685:filters
2616:Command
2515:Streams
2510:Signals
2281:Modular
2205:Asystem
1366:wounded
1321:wounded
1241:wounded
1205:wounded
1114:wounded
1078:wounded
774:glucose
693:lactose
675:glucose
648:express
636:lactose
618:glucose
591:express
579:express
513:lactose
188:where:
66:improve
2758:Visual
2725:System
2610:Action
2434:Strict
2166:
2098:
2040:
2007:
1968:
1943:
1924:
1870:
1860:
1336:canfly
1291:canfly
1148:canfly
1021:canfly
864:amount
819:amount
801:amount
768:amount
699:medium
687:amount
681:medium
669:amount
630:amount
612:amount
573:Enzyme
552:Enzyme
466:false
401:false
140:Syntax
3035:Roles
2918:Macro
2681:Pipes
2601:Array
2578:Query
2530:Logic
2439:GADTs
2429:Total
2352:Agent
2200:SCIFF
2175:(PDF)
2164:S2CID
2144:(PDF)
2114:(PDF)
1868:S2CID
1831:(PDF)
1813:Notes
1187:false
795:false
51:, or
2683:and
2330:list
2190:ACLP
2096:ISBN
1941:ISBN
1922:ISBN
1858:ISBN
1458:negp
1426:negp
1420:negp
1397:negp
1372:john
1357:john
1342:john
1327:mary
1312:mary
1297:mary
1247:john
1235:mary
1229:bird
1223:john
1217:bird
1163:bird
1120:john
1108:mary
1102:bird
1096:john
1090:bird
1036:bird
729:code
705:code
585:Gene
567:Gene
561:code
546:make
534:make
522:make
507:feed
398:is:
2588:DSL
2195:ACL
2156:doi
2128:doi
2073:doi
2048:doi
2015:doi
1976:doi
1850:doi
1666:is
1432:not
1414:not
1285:.
1075:):-
1063:)).
1048:not
780:low
759:low
735:lac
711:lac
654:lac
624:low
597:lac
454:and
450:and
446:and
436:and
432:and
105:ALP
3057::
2952:,
2948:,
2944:,
2750:,
2746:,
2475:,
2466:,
2345:,
2341:,
2328:,
2162:.
2152:11
2150:.
2146:.
2124:64
2122:.
2116:.
2069:44
2067:.
2063:.
2046:.
2034:34
2032:.
2013:.
1999:.
1991:;
1974:.
1960:.
1866:.
1856:.
1441:).
1429::-
1423:).
1411::-
1345:),
1330:).
1267:),
1250:).
1238:).
1226:).
1214:).
1202:),
1190::-
1184:).
1172:),
1160::-
1123:).
1111:).
1099:).
1087:).
1045:),
1033::-
867:).
843:V2
837:V1
834:),
831:V2
816:),
813:V1
798::-
783:).
765::-
750:).
744:),
726:).
720:),
702:).
684:),
666::-
663:))
645:).
642:hi
627:),
609::-
606:))
588:).
576:),
558::-
543:).
531:),
519::-
495:IC
468:if
442:if
428:if
422:if
403:if
344:if
338:if
253:.
237:.
55:,
47:,
2956:)
2940:(
2924:)
2920:(
2889:)
2885:(
2811:)
2807:(
2779:,
2774:,
2754:)
2742:(
2622:)
2618:(
2612:)
2608:(
2554:)
2550:(
2506:)
2502:(
2415:)
2411:(
2397:)
2393:(
2332:)
2324:(
2247:)
2243:(
2233:e
2226:t
2219:v
2158::
2134:.
2130::
2104:.
2081:.
2075::
2054:.
2050::
2021:.
2017::
2001:2
1982:.
1978::
1962:1
1949:.
1930:.
1874:.
1852::
1764:C
1761:I
1753:P
1710:C
1707:I
1648:P
1627:C
1624:I
1612:P
1591:G
1579:P
1536:G
1511:C
1508:I
1503:,
1500:A
1497:,
1494:P
1461:,
1452:,
1449:p
1438:p
1435:(
1417:(
1408:p
1400:,
1391:,
1388:p
1375:)
1369:(
1360:)
1354:(
1339:(
1324:(
1315:)
1309:(
1300:)
1294:(
1282:)
1279:_
1276:(
1264:_
1261:(
1244:(
1232:(
1220:(
1211:X
1208:(
1199:X
1196:(
1181:X
1178:(
1169:X
1166:(
1157:)
1154:X
1151:(
1140:)
1137:_
1134:(
1117:(
1105:(
1093:(
1084:X
1081:(
1072:X
1069:(
1060:X
1057:(
1051:(
1042:X
1039:(
1030:)
1027:X
1024:(
970:}
962:{
959:=
954:2
942:}
934:{
931:=
926:1
915:{
885:=
882:G
861:(
846:.
840:≠
828:,
825:S
822:(
810:,
807:S
804:(
777:,
771:(
762:)
756:(
741:z
738:(
732:(
717:y
714:(
708:(
696:,
690:(
678:,
672:(
660:X
657:(
651:(
639:,
633:(
621:,
615:(
603:X
600:(
594:(
582:(
570:,
564:(
555:)
549:(
537:(
525:(
516:)
510:(
491:A
487:P
384:C
381:I
359:A
321:P
296:C
293:I
288:,
285:A
282:,
279:P
251:G
246:G
242:G
235:G
231:G
202:.
176:,
170:C
167:I
164:,
161:A
158:,
155:P
103:(
91:)
85:(
80:)
76:(
62:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.