Logic Programming - a living formula Luís Moniz Pereira Centro de Inteligência Artificial, UNL FCT/UNL, 15 de Abril º

Overview zEvolution and reasoning zLogic and the computer zRole of AI in logic zWhat is happening with LP nowadays? zLogical based agents zInformation Ecosystems

Evolution and reasoning zEvolution has provided humans with: 4symbolic thought 4symbolic language communication abilities zThe pervasiveness of logic for knowledge representation and reasoning rests on its ability to promote: 4rational understanding 4common objectivity

Evolution and reasoning (2) zNew reasoning methods have been invented throughout human history: 3proof by contradiction 3transfinite induction 3recursion 3abduction 3contradiction removal 3etc. zLogic Programming and AI improve old methods, and create new reasoning methods

Logic and the computer zLogic provides a content independent formulation of the laws of thought zLogic articulates an intensional with an extensional view of predicates zThe language of logic is symbolic and its rules content-independent. So its workings can be specified by general, abstract rules These are programmable on the computer

Logic and the computer (2) zThe extensional and intensional views are reconciled in the computer by insisting that: This is the cornerstone of the Logic Programming paradigm  declarative semantics what is computed procedural computational semantics how it is computed

Role of AI in logic zAI aims to mechanize logic zAI intends to make explicit, and well-defined, the unconscious logic we use zAI contributes to stating and examining the problem of identifying limitations of symbolic reasoning methods zAI helps to explore new reasoning issues and methods, and to combine different reasoning abilities

Role of AI in logic (2) Problem: Classical logic was developed to study well-defined, consistent, and unchanging mathematical objects It acquired a static character zAI needs to deal with knowledge in flux, and less than perfect conditions, by means of more dynamic forms of logic

Role of AI in logic (3) zThus AI has developed logic beyond the confines of monotonic cumulativity typical of mathematical domains zAI has opened up logic to the non-monotonic real world domain of knowledge in flux: i.e. imprecise, incomplete, contradictory revisable, distributed, and evolving AI has added dynamics to the statics of logic

Logical tools zMuch of foregoing has been the focus of research in Logic Programming - LP - the field of AI which uses logic directly as a programming language What issues of the dynamics of logic has Logic Programming contributed to solve?

LP - Conclusion support zConclusions must be supported (caused) by the premises: yA close connection exists between LP implication and physical causality yLP implication is unidirectional C  P1,  N1 C  P2,  N2...

LP - Closed worlds zIf our information is complete: Problem: What if it is not complete ? C  P1,  N1 C  P2,  N2... C  V P,  N ii i 

LP - Open worlds zIn the real world, any setting is too complex to be defined exhaustively zUnforeseen exceptions may occur, based on new incoming information zIf we cannot prove a condition Ni, we may assume it false, but be prepared for subsequent information to the contrary

Open worlds - example can be coded as: faithful(H,K)  married(H,K),  lover(H,L) faithful(H,K)  married(H,K), not lover(H,L) where not Pred (default negation) may be read as: Pred is not provable The clause i.e. no proof for: lover(H,L)

LP - Defeasible Assumptions zDefault negation allows us to deal with lack of information zConclusions are not solid because the rules leading to them may be defeasible zLegal texts, regulations, and courts employ this form of negation abundantly It introduces non-monotonicity into knowledge representation

LP- Closed World Assumption zLet information be expressed positively: zIf no information is available about lovers then  lover(H,L) is true by CWA whereas lover(H,L) is false zThis asymmetry is undesirable, we should be able to write:  faithful(H,K)  married(H,K), not  lover(H,L) By CWA, if there is no derivable information about Pred we assume its negation

LP - Explicit negation zWhen neither positive nor negative information is derivable, we would like to say that both are false, epistemically zCWA and the above requisite can be reconciled by viewing , instead of classical negation, as a new form of negation: explicit negation The excluded middle postulate is unacceptable No excluded middle provision

LP - Explicit negation (2) zCWA can still be stated for exactly those predicates we wish, say P or  Q :  P  not P Q  not  Q So there is no loss

LP - Revising Assumptions zWe may combine the two viewpoints above: Problem: If married(H,K) is true, and with no information about lovers, then both faithful(H,K) and  faithful(H,K) are true! faithful(H,K)  married(H,K), not lover(H,L)  faithful(H,K)  married(H,K), not  lover(H,L)

LP - Revising Assumptions (2) zOur two assumptions: not lover(H,L) and not  lover(H,L) lead to a contradiction Problem: Which shall we retract ? They are equally preferable!

Undefinedness Solution: We retract both. We assume neither lover(H,L) nor  lover(H,L) false; instead, both become undefined For dealing with non-provability, we need a third truth-value to express our epistemic inability to come up with information

Undefinedness (2) zUndefinedness can be imposed with: Given no other information, we can now prove lover(H,L) and  lover(H,L) neither true nor false; cf. the WFS of logic programs lover(H,L)  not  lover(H,L)  lover(H,L)  not lover(H,L)

Updating in LP Another dimension to the dynamics of logic: Given a LP knowledge base, we must be able to update it with new incoming information, e.g. another LP DIs the resulting updated LP knowledge base ? DCan this process be iterated ? YES, we did it too! +

Static and dynamic worlds zMuch LP work has focussed on reasoning about a single world knowledge state zReasoning about world change and state transition is still being developed, namely: yknowledge updates yaction modelling More work on transitions and updates in LP is needed

Logical based agents  As computing systems become more distributed, interconnected, and open, intelligent agents will be a key technology zMENTAL project: We aim to establish, on a sound theoretical basis, the design of an overall LP architecture for mental agents

Logical based agents (2) zA mental agent must be able to: 4manage its knowledge, beliefs, intentions 4plan, as it receives new information and instructions 4react to changing conditions in the environment 4interact with other agents by exchanging messages 4react to other agents' requests

Agents evolution zAgents interact in increasingly complex worlds zNo longer possible to foresee and pre-program all possible situations zGeneralise from purely reactive agents to rational agents

Agents evolution (2) zAgents with complete knowledge and general abilities are not feasible zSpecialised agents4Cooperation between agents is in order

Logic programs for Agents zLP has developed KR mechanisms suitable for rational agents, e.g. More work on combining some or all of these mechanisms is needed 4Updates 4Condition-action rules 4Planning 4Argumentation 4Learning 4NMR mechanisms 4Taxonomies 4Abduction 4Belief revision 4Preferences

Going beyond agents Problem: In 10 years the available amount of information will be huge Humans will not be able to select and retrieve information with nowadays technology – World-Wide computing, mobile code, etc. Towards the notion of Information Ecosystem

Information Ecosystem (IE) zAn infohabitant of an IE is an entity – human or otherwise – with some rational abilities zAn IE has different kinds of infohabitants, distinguished by their reasoning or rational abilities zInfohabitants can access other computational entities – e.g. search engines, constraint solvers,...

Information Ecosystem (2) zInfohabitants communicate and cooperate with each other by means of reasoning and other rational means zThe IE monitors itself thus forming an ecosystem Logic as the language in the IE Logic for the laws of the IE

Information Ecosystem (3) zHumans have introduced logic for a number of purposes: for reasoning, for learning, … zHumans behave and act in a rational way zThe IE has to interact with humans Infohabitants must act within the IE on a rational logical basis

Conclusions AI, especially through LP, will continue to accomplish a good deal in identifying, formalizing, and implementing the laws of thought Most notably, AI via LP has taken on the challenge of opening up logic to the dynamics of knowledge in flux Continuing this work is essential if we are to cope, with the aid of computers, with the challenges of evermore accumulated and distributed knowledge, in a changing but rational information ecology