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Computational Logic and Cognitive Science: An Overview. Session 2: Cognitive Challenges ICCL Summer School 2008 Technical University of Dresden 26th of August, 2008 Helmar Gust & Kai-Uwe Kühnberger University of Osnabrück . Helmar Gust & Kai-Uwe Kühnberger Universität Osnabrück.

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computational logic and cognitive science an overview

Computational Logic and Cognitive Science: An Overview

Session 2: Cognitive Challenges

ICCL Summer School 2008

Technical University of Dresden

26th of August, 2008

Helmar Gust & Kai-Uwe Kühnberger

University of Osnabrück

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

overview
Overview
  • A Bunch of Cognitive Findings / Cognitive Challenges
    • Wason Selection Task
    • Remarks on Natural Language
    • Sizes of Cities
    • Theories of Mind
    • Creativity
    • Neuro-Symbolic Integration
    • Causality
    • Types of Reasoning
    • Cognitive Architectures

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

wason selection task
Wason Selection Task
  • The Wason selection task
    • 4 cards are given: On one side there is a number and on the other a letter printed.
    • Rule: If there is a vowel at one side, there will be an even number at the other side.
  • The following situation is given:

A D 4 7

  • The task is: Turn as few cards as possible to prove the rule.
    • The correct answer is to turn A and 7.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

wason selection task1
Wason Selection Task
  • The experiment was executed in various versions.
  • One showed the following results:
    • A and 4: 46 %
    • A: 33 %
    • A and 7: 3 %
    • Others: 18 %

Modus Tollens:

  • If p, then q. And: not q. Therefore: not p.
  • It seems to be the case that humans do not think logically…

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

wason selection task2
Wason Selection Task
  • New rule: Only people over 18 are allowed to drink alcohol.
    • Meaning: If for someone it is allowed to drink alcohol he/she must be over 18.
  • The new situation:

15 Water Beer 22

  • The solution is to turn Beer and 17.
  • This version of the Wason selection task seems to be much easier to solve for humans.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

wason selection task3
Wason Selection Task
  • Some proposals for an explanation of these results:
    • Humans do not think logical at all (Gigerenzer).
    • Humans think in models not in terms of logical deductions (Johnson-Laird).
    • Humans need to embed their reasoning in concrete situations. They have problems in reasoning in idealized situations, i.e. mental models do not reduce the problem to the idealized (abstracted) situation.
    • Humans can solve such problems, if it is placed in a social context (evolutionary psychology).
  • Many theories were proposed to model these data.
    • There are logic-based solutions as well as model-based solutions.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

wason selection task4
Wason Selection Task
  • Another important point to mention is the way to describe the task in natural language.
  • As a matter of fact, many logical connectives in natural language require a “more complex” interpretation than in classical logic.
    • “Peter is in the living room or in the kitchen.”
    • “Paul went to the university and gave a speech.” vs.“Paul gave a speech and went to the university.”
    • “If Jim works hard for the exam he will pass it.”
  • The standard version of the Wason selection task makes it plausible that a certain number of subjects interpret the implication as an equivalence.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

natural language
Natural Language
  • Natural language shows many features that cannot be easily modeled with classical logical approaches. Here are some examples:
    • “Many students read different books.”
      • Generalized quantifiers require an extension of classical logic.
    • “Could you tell me what time is it?”
      • Implicatures require a non-literal interpretation.
    • “Yesterday John told me that in 150 years Germany will have a Mediterranean climate.”
      • Temporal aspects require an extension of classical logic.
    • “If I had been on holidays two weeks ago, I would not have a burnout now.”
      • Counterfactuals
    • “The king of France is bald.”
      • Presuppositions extend the context in a non-trivial way, although there is nothing stated literally.
    • “I am here.”
      • Indexicals

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

san diego vs san antonio
San Diego vs. San Antonio
  • An experiment due to Goldstein & Gigerenzer (having to do with knowledge and rationality in general):
  • “Which city has more inhabitants: San Diego or San Antonio?”
    • This question was asked American students and German students.
    • Clearly German students knew little of San Diego, and many had never heard of San Antonio.
    • Results:
      • 62% of the American students answered correctly: San Diego.
      • 100% of the German students answered correctly: San Diego.
    • Gigerenzer proposes to use heuristics and cues to answer such questions resulting in a form of bounded rationality.
  • In any case, there is a certain tension between bounded rationality and classical logic and knowledge representation.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

theories of mind
Theories of Mind
  • Theories of Mind
    • Wise men problem (a variation of the famous muddy children problem).
    • “Three wise men know there are three red hats and two blue hats (and they know that all three know that). The king placed a hat on each wise man, such that no wise man knows which color his hat has. Then he asks each wise man in a row which color his hat has.”
    • Assume the first man says: “I don’t know.” and the second man says “I don’t know.” Why is it possible that the third man knows the color of his hat?

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

theories of mind1
Theories of Mind
  • BBB is impossible (there are only two blue hats).
  • P1 says: “I don’t know.”
    • P2 and P3 infer that P1 sees a red hat: RBB is impossible.
  • P2 says: “I don’t know.”
    • P3 infers that P2 sees a read hat: BRB is impossible.
    • P3 infers: P2 knows that P1 sees a red hat. In the remaining models there is only one where P3 has a blue hat: RRB. In this case P2 would know that she has a red hat.
  • Therefore P3 answers that he has a red hat.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

theories of mind2
Theories of Mind
  • Reasoning about the knowledge of other agents in a multi-agent systems seems to be natural to us.
    • Maybe this is controversial. Nevertheless, if put into a reasonable situation, probably we are quite good in solving such puzzles…
  • The frameworks proposed for representing and solving such puzzles are rather complicated.
    • Modal logic / epistemic logic
    • Situation theory
    • Game theory
  • In any case, classical logic needs to be extended in order to model reasoning about the beliefs of other agents.
    • It is quite plausible to assume that humans do not apply game theory or perform deductions according to a modal logic calculus in order to solve this problem. They probably solve such problems differently.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

creativity examples
Creativity: Examples

Jan van Eyck: The Arnolfini Marriage

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

creativity
Creativity
  • Creativity
    • It seems to be unquestionable that humans show creative behavior.
    • In particular, in problem solving, but also in using language productively (in particular, semantic productivity), in using metaphoric expressions, in generating theories, interpreting visual input, or making sense out of situations, humans show a remarkable ability of creativity.
    • There are no really good theories that can describe this kind of creativity. One candidate may be analogical reasoning.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

neuro symbolic integration
Neuro-Symbolic Integration
  • Symbolic-subsymbolic distinction
    • There is an obvious tension between symbolic and subsymbolic representations.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

neuro symbolic integration1
Neuro-Symbolic Integration
  • Some interesting facts about the symbolic-subsymbolic distinction and cognitive science
    • Classically natural language is considered to be a domain for symbolic theories.
    • Chomsky’s claim was that natural language cannot be learned without assuming a universal grammar.
      • His classical example was auxiliary inversion.
        • Ecuador is in South America.
        •  Is Ecuador in South America?
        • That woman who is walking her dog is Tom’s neighbor.
        •  *Is that woman who walking her dog is Tom’s neighbor?
        •  Is that woman who is walking her dog Tom’s neighbor?
    • Nevertheless important insights were provided by Elman who showed how rather simple recurrent networks (Elman networks) can learn correctly auxiliary inversion.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

neuro symbolic integration2
Neuro-Symbolic Integration
  • Some further remarks about the symbolic-subsymbolic distinction and cognitive science
    • A further interesting fact is that one of the currently most influential theories in linguistics was developed by the neuroscientist Paul Smolensky.
      •  Optimality theory.
    • Perhaps linguistics is a good testbed for neural modeling of complex data structures.
  • In total, the integration of symbolic theories (in particular logic) into neural networks is an ongoing challenge.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

causality
Causality
  • Causality seems to play an important role in human reasoning.
    • Although the concept of causality is complicated and not very well understood, humans tend to structure the dynamics of the world by causes and effects.
  • Reduction of causality to logical relations:
    • Mackie: Causality can be explained by insufficient and non-redundant parts of unnecessary but sufficient causes (INUS condition).
  • Example
    • Short circuit is the cause of the house burning down (plus side conditions): together these events are unnecessary but sufficient for the destruction; the short circuit is insufficient but non-redundant.
  • Nevertheless there are many different proposals for a logical reduction of causality, e.g. counterfactuals.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

reasoning aspects
Reasoning Aspects
  • Manifold of reasoning abilities:
    • Deductions, inductions, abductions, analogical reasoning, associations, non-monotonic reasoning etc.
    • An integration of these reasoning abilities is desirable.
    • From a pure logical approach this does not seem to be a straightforward task.
  • Even worse reasoning abilities are highly context dependent:
    • Humans have the ability to jump easily from one context to another context, finding re-interpretations of a given input, and applying different types of reasoning types.
  • Classical logical theories have their problems in modeling such situations.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

context dependencies
Context Dependencies

Suppose you are in a forest and you want to heat some water. You do not have a container of any kind. You can cut a vessel of wood, but it would burn in the fire. How can you heat the water in this wooden vessel? Kokinov & Petrov (2001)

Davies & Goel (2001)

“I am here.”

“Oh, it’s raining.”

“Every student answered every question.”

Indurkhya (1992)

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

non monotonicity
Non-Monotonicity

Axioms

Birds can usually fly.

Penguins are birds.

Tweety is a Penguin.

Theorem

Tweety can fly.

Axioms

Birds can usually fly.

Penguins are birds.

Tweety is a Penguin.

Penguins can’t fly.

Theorem

Tweety cannot fly.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

non monotonicity1
Non-Monotonicity

monotonic

extension

Theorems

Theorems

without p

Axioms

+ p

Axioms

new theorems

because of + p

Theorems

without p

non-monotonic

extension

Axioms

Theorems

incl. p

+ p

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

analogical reasoning
Analogical Reasoning

“Electrons are the planets of the atom.”

“Current is the water in an electric circuit.”

?

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

analogical reasoning1
Analogical Reasoning
  • Some statements about analogical reasoning right at the beginning:
    • Analogy making is in general not case-based reasoning.
    • Most interesting cases of analogies are cross-domain analogies.
    • Analogical reasoning can be modeled with logical means.
    • Analogical reasoning requires but cannot be reduced to deductions, inductions, and abductions.
    • Analogical reasoning is the core of human creativity.
  • A logical framework modeling analogical reasoning requires some non-standard techniques.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

cognitive architectures
Cognitive Architectures
  • The attempt to model cognitive behavior currently results in an inflationary number of different cognitive architectures.
    • Examples are: ACT-R (Anderson), SOAR (Laird), AMBR (Kokinov), Clarion (Sun), NARS (Wang), Icarus (Langely), PSI (Dörner, Bach) etc.
  • Some features of several (not of all) of these architectures:
    • Integration of different reasoning types.
    • “Non-rational” behaviors (associations, emotions etc.).
    • Hybrid (neuro-symbolic) representations.
      • Remark: not in the sense of neuro-symbolic integration, but more in the sense of “semantic networks + activation potentials”.
    • Integration of various cognitive abilities.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

what do we have so far
What Do We Have so Far?
  • Wason selection task
  • Remarks on Natural Language
  • San Diego vs. San Antonio
  • Theories of mind
  • Creativity
  • Symbolic-subsymbolic distinction
  • Causality
  • Reasoning
    • Context, non-monotonicity, analogy
  • Cognitive architectures

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

conclusion
Conclusion
  • The mentioned cognitive capacities (or deficiencies) are relatively hard to model with standard logic techniques.
  • The aim is to build intelligent systems that can come up with solutions of such problems.
  • This requires non-classical forms of reasoning, extensions of classical logic into various directions, and the integration of different reasoning mechanisms.

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008

thank you very much

Thank you very much!!

Helmar Gust & Kai-Uwe Kühnberger

Universität Osnabrück

ICCL Summer School 2008

Technical University of Dresden, August 25th – August 29th, 2008