Possible World Model

A Possible World Model is a world model that can represent alternative realities (to evaluate modal statements and counterfactual reasoning).

• AKA: Modal World, Possible Reality Model, Alternative World Representation.
• Context:
  • It can typically represent Modal Statement using formal structures that capture possibility, necessity, and contingency.
  • It can typically evaluate Truth Value of propositions across possible worlds using accessibility relations.
  • It can typically support Counterfactual Reasoning by modeling alternative scenarios that differ from actual world.
  • It can typically enable Modal Logic through formal semantics for modal operators like possibility and necessity.
  • It can typically formalize Philosophical Concepts such as metaphysical possibility, logical necessity, and causal dependence.
  • ...
  • It can often facilitate Thought Experiment by providing conceptual frameworks for exploring hypothetical scenarios.
  • It can often clarify Modal Claim through precise formulations and systematic evaluation.
  • It can often resolve Semantic Ambiguity in natural language statements containing modal terms.
  • It can often support Decision Theory by evaluating possible outcomes and their relative desirability.
  • ...
  • It can range from being a Propositional Possible World Model to being a First-Order Logic Possible World Model, depending on its expressive power.
  • It can range from being a Simple Possible World Model to being a Complex Possible World Model, depending on its structural complexity.
  • It can range from being a Discrete Possible World Model to being a Continuous Possible World Model, depending on its state space representation.
  • It can range from being a Classical Possible World Model to being a Non-Classical Possible World Model, depending on its underlying logic.
  • ...
  • It can be associated with Possible World Semantics for providing formal interpretations of modal language.
  • It can incorporate Accessibility Relation to define which possible worlds are accessible from other possible worlds.
  • It can utilize Kripke Structure with world sets, accessibility relations, and valuation functions.
  • It can employ Model Theoretic Approach for semantic interpretation of modal formulas.
  • ...
• Examples:
  • Philosophical Possible World Model Categories, such as:
    • Metaphysical Possible World Models, such as:
      • Lewisian Possible World Model for modal realism.
      • Actualist Possible World Model for ersatz theory.
      • Combinatorial Possible World Model for recombination theory.
    • Semantic Possible World Models, such as:
      • Kripkean Possible World Model for rigid designation.
      • Two-Dimensional Possible World Model for a priori possibility.
      • Montague Possible World Model for intensional semantics.
  • Logical Possible World Model Categories, such as:
    • Modal Logic Possible World Models, such as:
      • S5 Possible World Model for epistemic logic.
      • Deontic Possible World Model for normative reasoning.
      • Temporal Possible World Model for tense logic.
    • Non-Classical Possible World Models, such as:
      • Intuitionistic Possible World Model for constructive logic.
      • Many-Valued Possible World Model for fuzzy modal logic.
      • Paraconsistent Possible World Model for inconsistency-tolerant reasoning.
  • Application Domain Categories, such as:
    • Artificial Intelligence Possible World Models, such as:
      • Planning Possible World Model for goal-directed reasoning.
      • Belief Revision Possible World Model for knowledge update.
      • Natural Language Possible World Model for modal statement interpretation.
  • ...
• Counter-Examples:
  • Situation Semantics, which models partial states rather than complete possible worlds.
  • Probability Models, which represent likelihood distributions rather than modal possibility.
  • Single World Models, which lack alternative world representations needed for modal reasoning.
  • Causal Models, which focus on cause-effect relations rather than modal properties.
  • Extensional Logics, which operate only on actual truth values without possible world semantics.
• See: Modal Logic, Counterfactual Statement, Conditional Logic, Thought Experiment, Abductive Reasoning, Possible World, Modal Realism, Kripke Semantics.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/possible_world Retrieved:2015-11-17.
  • In philosophy and logic, the concept of a possible world is used to express modal claims. The concept of possible worlds is common in contemporary philosophical discourse but has been disputed.

2015

• (Russell, 2015) ⇒ Stuart Russell. (2015). “Unifying Logic and Probability.” In: Communications of the ACM Journal, 58(7). doi:10.1145/2699411
  • QUOTE: This section explains the core concepts of logic and probability, beginning with possible worlds. A possible world is a formal object (think “data structure") with respect to which the truth of any assertion can be evaluated.

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