Possible World Model
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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.
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- 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.
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- 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.
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- 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.
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- Examples:
- Philosophical Possible World Model Categories, such as:
- Metaphysical Possible World Models, such as:
- Semantic Possible World Models, such as:
- Logical Possible World Model Categories, such as:
- Modal Logic Possible World Models, such as:
- Non-Classical Possible World Models, such as:
- Application Domain Categories, such as:
- ...
- Philosophical Possible World Model Categories, such as:
- 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.
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.