model-checker 0.2.20

A hyperintensional model checker for counterfactual conditionals

Model Checker

This project draws on the Z3 theorem prover to provide tools for proving theorems and finding countermodels for counterfactual conditional and modal claims.

Detailed installation instructions are provided in the GitHub repository.

Instructions

To generate a test file run model-checker without arguments.

Alternatively, run model-checker path/to/test_file.py if the test_file.py already exists.

A number of examples are provided in the GitHub repository.

Each file must specify a set of premises which are treated conjunctively, conclusions which are treated disjunctively, and the number N of atomic states to include in each model.

Optionally, the user can specify whether to print the Z3 constraints when a model is found, or the unsatisfiable core when no model exists, as well as an option to save the output.

Syntax

The language currently includes operators for the counterfactual conditional boxright, modal operators for necessity Box and possibility Diamond, and the extensional operators for conjunction wedge, disjunction vee, material conditional rightarrow, material biconditional leftrightarrow, and negation neg.

Semantics

The semantics included is hyperintensional insofar as sentences are evaluated at states which may be partial rather than total as in intensional semantic theories. States are modeled by bitvectors of a specified length (e.g., #b00101 has length 5), where state fusion is modeled by the bitwise OR operator |. For instance, #b00101 | #b11001 = #b11101. The atomic states have exactly one occurrence of 1 and the null state has no occurrences of 1. The space of states is closed under fusion and finite.

States are named by lowercase letters for the sake of printing readable countermodels. A state a is part of a state b just in case a | b = b. States may be either possible or impossible where the null state is required to be possible and every part of a possible state is possible. The states a and b are compatible just in case a | b is possible. A world state is any state that is both possible and includes every compatible state as a part.

Sentences are assigned verifier states and falsifier states where the both the verifiers and falsifiers are required to be closed under fusion. True counterfactual and modal sentences are verified by the null state and falsified by no states. Negated sentences are verified by the falsifiers for the sentence negated and falsified by the verifiers for the sentence negated. Conjunctions are verified by the pairwise fusions of verifiers for the conjuncts and falsified by falsifiers for either of the conjuncts or fusions thereof. Conjunction and disjunction are dual operators obeying the standard De Morgan laws. The absorption laws do not hold, nor does conjunction distribute over disjunction, or vice versa.

The semantic theory for counterfactual conditionals is motivated and further elaborated in this draft. For the background theory of hyperintensional propositions, see this paper. More information can be found in the GitHub repository.