dfs_main.pl -- Distributional Formal Semantics

A library for Distributional Formal Semantics (DFS).

To be done

- Elaborate on DFS.

 dfs_version_major(-MajorVersion)

Major version number.

 dfs_version_minor(-MinorVersion)

Minor version number.

 dfs_version_patch(-PatchVersion)

Patch version number.

 dfs_main

Module entry point.

Re-exported predicates

The following predicates are re-exported from other modules

 dfs_conjoin(+FormulaSet, -Conjunction) is det

True if Conjunction is a logical conjunction of the formulas in FormulaSet.

 dfs_interpret(+Formula, +Model, +G) is semidet

dfs_interpret(+FormulaSet, +Model, +G) is semidet

Evaluates the truth value of Formula in Model, given the assignment function G.

 dfs_inference_score(+Vector1, +Vector2, -Score) is det

 dfs_inference_score(+Formula1, +Formula2, +ModelSet, -Score) is det

dfs_inference_score(+Formula1, +Formula2, +ModelMatrix, -Score) is det

Inference score of P from Q, where P and Q are either vectors or formulas.

           | (Pr(P|Q) - Pr(P)) / (1 - Pr(P))    iff Pr(P|Q) > Pr(P)
inf(P,Q) = |
           | (Pr(P|Q) - Pr(P)) / Pr(P)          otherwise

 dfs_terms_to_entities(?Terms, +TermInstantiations, ?Entities) is det

Maps Terms into Entities (or vice versa), given their instantiations.

 dfs_map_discourse_onto_semantics(+SenSemTuples, +WVecs, +ModelSet, -Mappings) is det

Mappings is a list of quadruples (Sen,Sem,[SenVecs],[SemVec]), where SenVecs is a word-by-word vector-based mapping of a sentence (Sen) onto single SemVec, a vector representation of its semantics (Sem).

See also

- dfs_map_sentence_onto_semantics/4

 dfs_constant_instantiations(+Model, -ConstantInstantiations) is det

ConstantInstantiations is a list of all constant instantiations in Model.

 dfs_conj_probability(+Vector1, +Vector2, -ConjPr) is det

 dfs_conj_probability(+Formula1, +Formula2, +ModelSet, -ConjPr) is det

dfs_conj_probability(+Formula1, +Formula2, +ModelMatrix, -ConjPr) is det

Conjunction probability of P and Q, where P and Q are either vectors or formulas.

Pr(P&Q) = sum_i(v_i(P&Q)) / |M|

 dfs_semantic_entropy(+Prefix, +ModelSet, -Entropy) is det

Semantic entropy for a prefix.

H(w_i) = - sum_(foreach s in S) Pr(s|v(w_1...i))
         * log(Pr(s|v(w_1...i)))

where v(w_1...i) is the disjunction of all semantics consistent with the prefix w_1...w_i.

 dfs_matrix_to_models(+ModelMatrix, -ModelSet) is det

Convert a vector space into a set of models.

See also

- dfs_vector_to_model/2.

 drs_to_fol(+DRS, -Formula) is det

Translate DRS into a first-order logic Formula.

 coals_padded_binary_vectors(+WindowType, +WindowSize, +NHotPaddingBits, -CoalsVectors) is det

CoalsVectors is a list of (Word,Vector) tuples, where Vector is a binary COALS vector, derived from a DCG using a WindowType of WindowSize. Binary vectors are padded with a a minimal binary identifier containing NHotPaddingBits, in such a way that the identifiers for similar binary vectors do not share any features.

 dfs_syntactic_surprisal(+Word, +Prefix, -Surprisal) is det

Syntactic surprisal of a word given a prefix.

S(w_i+1) = -log(P(w_i+1|w_1...i))
         = log(P(w_1...i)) - log(P(w_1...i+1))
         = log(freq(w_1...i)) - log(freq(w_1...i+1))

 mesh_write_atomic_prop_set(+ModelSet, +File) is det

Write a MESH-readable set of atomic propositions:

Dimensions # #

BeginItem
Name "sentence"
Meta "semantics"
Input # # # Target # #
Input # # # Target # #
EndItem

For each atomic proposition, the input vector is the zero vector with number of dimensions equal to the number of words produced by dfs_words/1, and the target vector is the vector encoding the atomic proposition.

 dfs_pprint_entailments(+Entailments) is det

Pretty print entailments.

 +ModelSet @># -Matrix is det

Infix operator for dfs_models_to_matrix/2.

See also

- dfs_models_to_matrix/2.

 dfs_sentence_sentence_mappings(+InWVecs, +OutWVecs, -Mappings) is det

Mappings is a list of quadruples (Sen,Sem,[InSenVecs],[OutSenVecs]).

See also

- dfs_map_sentence_onto_sentence/4.

 dfs_surprisal(+Vector1, +Vector2, -Surprisal) is det

 dfs_surprisal(+Formula1, +Formula2, +ModelSet, -Surprisal) is det

dfs_surprisal(+Formula1, +Formula2, +ModelMatrix, -Surprisal) is det

Surprisal of P given Q, where P and Q are either vectors or formulas.

surprisal(P,Q) = -log Pr(P|Q)

 dfs_pprint_model(+Model) is det

Pretty print a model.

 dfs_sentence_semantics_mappings(+WVecs, +ModelSet, -Mappings) is det

Mappings is a list of quadruples (Sen,Sem,[SenVecs],[SemVec]).

See also

- dfs_map_sentence_onto_semantics/4

 dfs_logical_equivalence(+FormulaP, +FormulaQ, +ModelSet) is det

dfs_logical_equivalence(+FormulaP, +FormulaQ, +ModelMatrix) is det

A formula P is logically equivalent to formula Q iff [[P]]^M,g = [[Q]]^M,g for all models M and variable assignments g

 dfs_read_models(+File, -ModelSet) is det

Reads ModelSet from File.

 dfs_conj_vector(+Vector1, +Vector2, -ConjVector) is det

ConjVector is the conjunction (component-wise product) of Vector1 and Vector2.

 dfs_sentences(-SenSemTuples) is det

SenSemTuples is a list of all sentence-semantics mappings generated.

 dfs_sample_models(+NumModels, -ModelSet) is det

ModelSet is a set of NumModels sampled models.

See also

- dfs_sample_model.

 dfs_discourse_semantics_mappings(+WVecs, +ModelSet, -Mappings) is det

Mappings is a list of lists of (Sen,Sem,[SenVecs],[SemVec]) quadruples.

See also

- dfs_map_discourse_onto_semantics/4

 dfs_interpret(+Formula, +Model) is semidet

dfs_interpret(+FormulaSet, +Model) is semidet

Evaluates the truth value of Formula in Model, given an initial assignment function G.

 dfs_assign(+G, +Model, +Assignments, -Gprime) is det

Updates the assignment function G of Model with variable Assignments, yielding assignment function G'.

 dfs_cond_probability(+Vector1, Vector2, -ConjPr) is det

 dfs_cond_probability(+Formula1, +Formula2, +ModelSet, -CondPr) is det

dfs_cond_probability(+Formula1, +Formula2, +ModelMatrix, -CondPr) is det

Conditional probability of P given Q, where P and Q are either vectors or formulas.

Pr(P|Q) = Pr(P&Q) / Pr(Q)

 dfs_prior_probability(+Vector, -PriorPr) is det

 dfs_prior_probability(+Formula, +ModelSet, -PriorPr) is det

dfs_prior_probability(+Formula, +ModelMatrix, -PriorPr) is det

Prior probability of P, where P is either a vector or a formula.

Pr(P) = sum_i(v_i(P)) / |M|

 coals_binary_vectors(+WindowType, +WindowSize, -CoalsVectors) is det

CoalsVectors is a list of (Word,Vector) tuples, where Vector is a binary COALS vector, derived from a DCG using a WindowType of WindowSize. Binary COALS vectors are derived from real-valued COALS vectors, by setting positive correlations to hot bits (i.e., 1s).

 dfs_delta_entropy(+Vector1, +Vector2, -DeltaH) is det

 dfs_delta_entropy(+Formula1, +Formula2, +ModelSet, -DeltaH) is det

dfs_delta_entropy(+Formula1, +Formula2, +ModelMatrix, -DeltaH) is det

Entropy delta of P given Q, where P and Q are either vectors or formulas.

DH(P,Q) = H(Q) - H(P)

 dfs_entities(+N, -Entities) is det

Entities is a list of N model entities.

 dfs_semantic_surprisal(+Word, +Prefix, +ModelSet, -Surprisal) is det

Semantic suprisal for a word given a prefix.

S(w_i+1) = -log(Pr(v(w_1...i+1)|w_1...i))

where v(w_1...i) is the disjunction of all semantics consistent with the prefix w_1...w_i.

 dfs_vector_to_model(+ModelVector, -Model)

Converts ModelVector, a set of tuples (AtomicProp,State) representing the State of each atomic proposition AtomicProp, into a Model.

 +Matrix #>@ -ModelSet is det

Infix operator for dfs_matrix_to_models/2.

See also

- dfs_matrix_to_models/2.

 dfs_pprint_constraints is det

Pretty print model constraints.

 dfs_entropy(+Vector, -Entropy) is det

 dfs_entropy(+Formula, +ModelSet, -Entropy) is det

dfs_entropy(+Formula, +ModelMatrix, -Entropy) is det

Entropy of P, where P is either a vector or a formula.

H(P) = - sum_{s in S} Pr(s|P) * log Pr(s|P)

where the set S consists of all possible points in the DFS space that are fully specified with respect to the atomic propositions; that is, each point s in S constitutes a unique logical combination of all atomic propostions.

 dfs_pprint_formula(+Formula) is det

Pretty print a first-order logic formula.

 dfs_prefix_continuations(+Prefix, SemSenMappings) is det

SemSenMappings is a list of all tuples (Sen,Sem), where sentence Sen is a possible continuation of Prefix, and Sem its corresponding FOL semantics.

 dfs_entailment(+FormulaP, +FormulaQ, +ModelSet) is det

dfs_entailment(+FormulaP, +FormulaQ, +ModelMatrix) is det

A formula P entails a formula Q (P |= Q) iff Q is true in every model that satisfies P.

 dfs_write_models(+ModelSet, +File) is det

Writes ModelSet to File.

 dfs_complement(+Formula, +ComplementFormula) is det

ComplementFormula specifies the falsehood conditions of Formula.

 dfs_sample_model(-Model) is det

Sample a model from the world specificiations.

 dfs_words(-Words) is det

Words is the set of all lexical items generated.

 dfs_map_semantics_onto_sentence(+SenSemTuple, +WVecs, +ModelSet, -Mapping) is det

Mapping is a quadruple (Sen,Sem,[SemVec],[SenVecs]), where SemVec is a vector representation of a sentence semantics (Sem), and SenVecs a word-by-word vector-based representation of the corresponding sentence (Sen).

Word vector representation (WVecs) are pre-specified (e.g., using dfs_localist_word_vectors/2), and a vector representation of the sentence meaning, specified by the formula Sem, is derived from ModelSet.

 dfs_formulas_to_fol(+Formulas, -FOLFormulas) is det

Convert FOL and/or DRS formulas into first-order logic formulas.

 dfs_cond_probability(+Vector1, Vector2, -ConjPr) is det

 dfs_cond_probability(+Formula1, +Formula2, +ModelSet, -CondPr) is det

dfs_cond_probability(+Formula1, +Formula2, +ModelMatrix, -CondPr) is det

Conditional probability of P given Q, where P and Q are either vectors or formulas.

Pr(P|Q) = Pr(P&Q) / Pr(Q)

 dfs_init_g(+Model, -G) is det

Initializes the assignment function G :: Var -> Um. Variables are assigned by iterating over the entities in the Model universe.

 dfs_prior_probability(+Vector, -PriorPr) is det

 dfs_prior_probability(+Formula, +ModelSet, -PriorPr) is det

dfs_prior_probability(+Formula, +ModelMatrix, -PriorPr) is det

Prior probability of P, where P is either a vector or a formula.

Pr(P) = sum_i(v_i(P)) / |M|

 dfs_variables(-Variables) is det

Variables is a list of variables.

 coals_vectors(+WindowType, +WindowSize, -CoalsVectors) is det

CoalsVectors is a list of (Word,Vector) tuples, where Vector is a real-valued COALS vector, derived from a DCG using a WindowType of WindowSize.

 dfs_syntactic_delta_entropy(+Word, +Prefix, -DeltaH) is det

Syntactic entropy delta for a word given a prefix.

DH(w_i+1) = H(w_i) - H(w_i+1)

 dfs_models_to_matrix(+ModelSet, -ModelMatrix) is det

Convert a set of models into a vector space.

See also

- dfs_model_to_vector/2.

 dfs_coordinates(+Interpretation, -Coordinates) is semidet

Coordinates designates the point in space in between the elements of Interpretation.

 dfs_entropy(+Vector, -Entropy) is det

 dfs_entropy(+Formula, +ModelSet, -Entropy) is det

dfs_entropy(+Formula, +ModelMatrix, -Entropy) is det

Entropy of P, where P is either a vector or a formula.

H(P) = - sum_{s in S} Pr(s|P) * log Pr(s|P)

where the set S consists of all possible points in the DFS space that are fully specified with respect to the atomic propositions; that is, each point s in S constitutes a unique logical combination of all atomic propostions.

 dfs_entailments(+Interpretation, +ModelSet, -Entailments) is semidet

Entailments is a set of (Element,AtomicProps) tuples, such that each AtomicProps is a list of atomic propositions entailed by the corresponding Element in Interpretation.

 dfs_prefix_frequency(+Prefix, -Frequency) is det

Frequency is the occurence frequency of sentence Prefix.

 dfs_semantics_sentence_mappings(+WVecs, +ModelSet, -Mappings) is det

Mappings is a list of quadruples (Sen,Sem,[SemVec],[SenVecs]).

See also

- dfs_map_semantics_onto_sentence/4

 dfs_pprint_matrix(+ModelMatrix) is det

Pretty print ModelMatrix.

 dfs_read_matrix(+File, -ModelMatrix) is det

Read ModelMatrix from File.

 dfs_map_semantics_onto_discourse(+SenSemTuples, +WVecs, +ModelSet, -Mappings) is det

Mappings is a list of quadruples (Sen,Sem,[SemVec],[SenVecs]), where SemVec is a vector representation of a sentence semantics (Sem), and SenVecs a word-by-word vector-based representation of the corresponding sentence (Sen).

See also

- dfs_map_semantics_onto_sentence/4

 dfs_satisfiability(+Formula, +ModelSet) is det

dfs_satisfiability(+Formula, +ModelMatrix) is det

A formula P is satisfiable iff P is true in at least one model M.

 dfs_localist_word_vectors(-WordVectors) is det

WordVectors is a list of tuples (Word,Vector) where Vector is a localist vector representation for each Word generated.

 dfs_sample_models_mt(+NumThreads, +NumModels, -ModelSet) is det

ModelSet is a set of NumThreads * NumModels sampled models.

See also

- dfs_sample_model.

 dfs_disjoin(+FormulaSet, -Disjunction) is det

True if Disjunction is a logical disjunction of the formulas in FormulaSet.

 dfs_discourse(SenSemTuples) is det

SenSemTuples is a list of all discourse sentence-semantics mappings.

 dfs_formula_to_fol(+Formula, -FOLFormula) is det

Convert FOL and/or DRS formula into first-order logic formula.

 dfs_conj_probability(+Vector1, +Vector2, -ConjPr) is det

 dfs_conj_probability(+Formula1, +Formula2, +ModelSet, -ConjPr) is det

dfs_conj_probability(+Formula1, +Formula2, +ModelMatrix, -ConjPr) is det

Conjunction probability of P and Q, where P and Q are either vectors or formulas.

Pr(P&Q) = sum_i(v_i(P&Q)) / |M|

 dfs_term_instantiations(+Model, +G, -TermInstantiations) is det

TermInstantiations is a list of all constant and variable instantiations in Model.

 dfs_inference_score(+Vector1, +Vector2, -Score) is det

 dfs_inference_score(+Formula1, +Formula2, +ModelSet, -Score) is det

dfs_inference_score(+Formula1, +Formula2, +ModelMatrix, -Score) is det

Inference score of P from Q, where P and Q are either vectors or formulas.

           | (Pr(P|Q) - Pr(P)) / (1 - Pr(P))    iff Pr(P|Q) > Pr(P)
inf(P,Q) = |
           | (Pr(P|Q) - Pr(P)) / Pr(P)          otherwise

 coals_write_vectors(+Tuples, +File) is det

Writes a list of (Word,Vector) Tuples to File in CSV format.

 dfs_vector(+Formula, +ModelSet, -Vector) is det

dfs_vector(+Formula, +ModelMatrix, -Vector) is det

A formula P is true in a model M iff [[P]]^M,g = 1 given an arbitrary variable assignment g.

 mesh_write_set(+SentenceSemanticsMappings, +File) is det

mesh_write_set(+DiscourseSemanticsMappings, +File) is det

Write all sentence-semantics, semantics-sentence, discourse-semantics, semantics-discourse, or sentence-sentence Mappings to File in MESH-readable format. Files start with a dimensions specification:

Dimensions # #

where the first '#' is an integer indicating the input vector size, and the second '#' an integer indicating target vector size. The remainder of the file consists of item blocks:

Sentences format:

BeginItem
Name "sentence"
Meta "semantics"
Input # # # Target # #
Input # # # Target # #
EndItem

[...]

where 'sentence' is a sentence, and 'semantics' its formatted FOL semantics. The '#'s are the integer units of the input/target vectors.

Discourse format:

BeginItem
Name "sentence1 #### sentence2"
Meta "semantics1 #### semantics2"
Input # # # Target # #
Input # # # Target # #
EndItem

[...]

where 'sentence1' and 'sentence2' are sentences of a discourse, and 'semantics1' and 'semantics2' the (possibly) varying semantics for the two sentences. The single '#'s are the integer units of the input/target vectors, and the '####' string is a sentence divider.

 dfs_syntactic_entropy(+Prefix, -Entropy) is det

Syntactic entropy for a prefix.

H(w_i) = -sum_(w_1...i,w_i+1...n)
         Pr(w_1...i,w_i+1...n|w_1...i)
         * log(Pr(w_1...i,w_i+1...n|w_1...i))

 drs_interpret(+DRS, +ModelSet, -Vector) is det

drs_interpret(+DRS, +ModelMatrix, -Vector) is det

A DRS K is true in a model M iff [[K]]^M,g = 1 given an arbitrary variable assignment g.

 dfs_semantic_delta_entropy(+Word, +Prefix, +ModelSet, -DeltaH) is det

Semantic entropy delta for a word given a prefix.

DH(w_i+1) = H(w_i) - H(w_i+1)

 dfs_semantics(+Formula, +ModelSet, -Interpretation) is semidet

Derives an Interpretation (a set of points in DFS space) for Formula given ModelSet.

 dfs_delta_entropy(+Vector1, +Vector2, -DeltaH) is det

 dfs_delta_entropy(+Formula1, +Formula2, +ModelSet, -DeltaH) is det

dfs_delta_entropy(+Formula1, +Formula2, +ModelMatrix, -DeltaH) is det

Entropy delta of P given Q, where P and Q are either vectors or formulas.

DH(P,Q) = H(Q) - H(P)

 dfs_map_sentence_onto_sentence(+SenSemTuple, +InWVecs, +OutWVecs, -Mapping) is det

Mapping is a quadruple (Sen,Sem,[InSenVecs],[OutSenVecs]), where InSenVecs and OutSenVecs are word-by-word vector-based representations of the corresponding sentence (Sen).

 dfs_sentence_frequency(+Sentence, -Frequency) is det

Frequency is is the occurrence frequency of Sentence.

 dfs_model_to_vector(+Model, -ModelVector) is det

ModelVector is a set of tuples (AtomicProp,State) representing the State of each atomic proposition AtomicProp in Model.

 dfs_surprisal(+Vector1, +Vector2, -Surprisal) is det

 dfs_surprisal(+Formula1, +Formula2, +ModelSet, -Surprisal) is det

dfs_surprisal(+Formula1, +Formula2, +ModelMatrix, -Surprisal) is det

Surprisal of P given Q, where P and Q are either vectors or formulas.

surprisal(P,Q) = -log Pr(P|Q)

 dfs_pprint_propositions(+Model) is det

Pretty print the propositions of Model.

 dfs_write_matrix(+ModelMatrix, +File) is det

Write ModelMatrix to File.

 dfs_validity(+Formula, +ModelSet) is det

dfs_validity(+Formula, +ModelMatrix) is det

A formula P is valid (|= P) iff P is true (not false) in all models.

 dfs_map_sentence_onto_semantics(+SenSemTuple, +WVecs, +ModelSet, -Mapping) is det

Mapping is a quadruple (Sen,Sem,[SenVecs],[SemVec]), where SenVecs is a word-by-word vector-based mapping of a sentence (Sen) onto single SemVec, a vector representation of its semantics (Sem).

Word vector representation (WVecs) are pre-specified (e.g., using dfs_localist_word_vectors/1), and a vector representation of the sentence meaning, specified by the formula Sem, is derived from ModelSet.

 dfs_semantics_discourse_mappings(+WVecs, +ModelSet, -Mappings) is det

Mappings is a list of lists of quadruples (Sen,Sem,[SemVec],[SenVecs]).

See also

- dfs_map_semantics_onto_discourse/4