Table of Links Abstract and Introduction
SylloBio-NLI
Empirical Evaluation
Related Work
Conclusions
Limitations and References A. Formalization of the SylloBio-NLI Resource Generation Process B. Formalization of Tasks 1 and 2 C. Dictionary of gene and pathway membership D. Domain-specific pipeline for creating NL instances and E Accessing LLMs F. Experimental Details G. Evaluation Metrics H. Prompting LLMs - Zero-shot prompts I. Prompting LLMs - Few-shot prompts J. Results: Misaligned Instruction-Response K. Results: Ambiguous Impact of Distractors on Reasoning L. Results: Models Prioritize Contextual Knowledge Over Background Knowledge M Supplementary Figures and N Supplementary Tables A Formalization of the SylloBio-NLI Resource Generation Process This appendix formalises the generation process of the syllogistic inference patterns. We start by defining the mains constructs (formal and linguistic artefacts and functions) of the underlying framework: Syllogistic Scheme (S): A logical inference pattern consisting of premises and a conclusion, S = {P1, P2, . . . , Pn, C}, where Pi is premise i and C is the conclusion.


Formal Argument Scheme (σ): Representation of a syllogistic scheme in first-order logic (FOL), σ(S) = {ϕ1, ϕ2, . . . , ϕn, ψ}, where ϕi corresponds to Pi and ψ corresponds to C.


Natural Language Template (τ ): A natural language schema mapping each formula in σ(S) to a sentence template, τ (σ(S)) = {τ1, τ2, . . . , τn, σ}, where τi is the sentence template for ϕi and σ is the sentence template for ψ.


Ontology (O): A domain-specific knowledge base containing entities E and predicates Π, O = {E, Π}, where E = {e1, e2, . . . , ek} and Π = {π1, π2, . . . , πl}.


Instantiation Function (I): A function that replaces placeholders in τ with entities and predicates from O, I : τ (σ(S)) × O → NL, where NL is the set of natural language sentences.


Expert Mapping Function (µExpert): A function provided by a domain expert to map placeholders to appropriate ontology terms, µExpert : Placeholders → E ∪ Π.


Knowledge Base (KB): A collection of instantiated syllogistic arguments, KB = {A1, A2, . . . , Am}, where Ai = {P ′ 1 , P′ 2 , . . . , P′ n , C′} and P ′ i , C′ are instantiated natural language sentences. A.1 Process Formalisation The process formalisation defines a systematic process for generating domain-specific syllogistic arguments by: 1. Defining formal representations of syllogistic schemes in first-order logic. Generating natural language templates from these formal representations.


Mapping placeholders to domain-specific entities and predicates using an ontology and expert knowledge.


Instantiating the templates to produce logically valid and semantically sound arguments.


Constructing a knowledge base for evaluating NLI models. This ensures that the generated arguments are both logically valid and contextually relevant to the biomedical domain. Input: A set of syllogistic schemes: S = {S1, S2, . . . , Sm}, an ontology: O = {E, Π}, an expert mapping function: µExpert. Output: A knowledge base of instantiated arguments: KB. Step 1: Formal Argument Scheme Selection: For each syllogistic scheme Si ∈ S, define its formal argument scheme in first-order logic: Step 2: Natural Language Template Generation: Transform each formula in σ(Si) into a natural language template: Step 3: Ontology Mapping and Instantiation: Apply the expert mapping function to select appropriate entities and predicates from the ontology: Instantiate the templates: under the following constraints: • Logical Validity: The instantiated arguments must preserve the logical structure of σ(Si). • Domain Soundness: The selected entities and predicates must be semantically coherent within the targeted subdomain. These constraints can be further formalised as: Logical Validity Constraint: The instantiated argument Ai must be logically valid: {ϕ ′ 1 , ϕ′ 2 , . . . , ϕ′ n} |= ψ ′ , where ϕ ′ j corresponds to the logical form of P ′ j . Domain Soundness Constraint: The entities and predicates used must be semantically valid within the domain: ∀e ∈ E ′ , π ∈ Π ′ , DomainValid(e, π) = True, where E′ ⊆ E and Π′ ⊆ Π are entities and predicates used in Ai Verification of Logical Validity: Ensure that the instantiated premises logically entail the conclusion: {ϕ ′ 1 , ϕ′ 2 , . . . , ϕ′ n} |= ψ ′ , using logical inference rules. Verification of Domain Soundness: Confirm that: • All entities and predicates are correctly used. • There are no semantic contradictions. Step 4: Knowledge Base Construction: Aggregate all instantiated arguments into the knowledge base: This is summarised with the following algorithmic outline: Authors:
(1) Magdalena Wysocka, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom;
(2) Danilo S. Carvalho, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom and Department of Computer Science, Univ. of Manchester, United Kingdom;
(3) Oskar Wysocki, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom and ited Kingdom 3 I;
(4) Marco Valentino, Idiap Research Institute, Switzerland;
(5) André Freitas, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom, Department of Computer Science, Univ. of Manchester, United Kingdom and Idiap Research Institute, Switzerland. This paper is available on arxiv under CC BY-NC-SA 4.0 license. Table of Links Abstract and Introduction SylloBio-NLI Empirical Evaluation Related Work Conclusions Limitations and References Abstract and Introduction Abstract and Introduction SylloBio-NLI SylloBio-NLI Empirical Evaluation Empirical Evaluation Related Work Related Work Conclusions Conclusions Limitations and References Limitations and References A. Formalization of the SylloBio-NLI Resource Generation Process A. Formalization of the SylloBio-NLI Resource Generation Process B. Formalization of Tasks 1 and 2 B. Formalization of Tasks 1 and 2 C. Dictionary of gene and pathway membership C. Dictionary of gene and pathway membership D. Domain-specific pipeline for creating NL instances and E Accessing LLMs D. Domain-specific pipeline for creating NL instances and E Accessing LLMs F. Experimental Details F. Experimental Details G. Evaluation Metrics G. Evaluation Metrics H. Prompting LLMs - Zero-shot prompts H. Prompting LLMs - Zero-shot prompts I. Prompting LLMs - Few-shot prompts I. Prompting LLMs - Few-shot prompts J. Results: Misaligned Instruction-Response J. Results: Misaligned Instruction-Response K. Results: Ambiguous Impact of Distractors on Reasoning K. Results: Ambiguous Impact of Distractors on Reasoning L. Results: Models Prioritize Contextual Knowledge Over Background Knowledge L. Results: Models Prioritize Contextual Knowledge Over Background Knowledge M Supplementary Figures and N Supplementary Tables M Supplementary Figures and N Supplementary Tables A Formalization of the SylloBio-NLI Resource Generation Process This appendix formalises the generation process of the syllogistic inference patterns. We start by defining the mains constructs (formal and linguistic artefacts and functions) of the underlying framework: Syllogistic Scheme (S): A logical inference pattern consisting of premises and a conclusion, S = {P1, P2, . . . , Pn, C}, where Pi is premise i and C is the conclusion. Formal Argument Scheme (σ): Representation of a syllogistic scheme in first-order logic (FOL), σ(S) = {ϕ1, ϕ2, . . . , ϕn, ψ}, where ϕi corresponds to Pi and ψ corresponds to C. Natural Language Template (τ ): A natural language schema mapping each formula in σ(S) to a sentence template, τ (σ(S)) = {τ1, τ2, . . . , τn, σ}, where τi is the sentence template for ϕi and σ is the sentence template for ψ. Ontology (O): A domain-specific knowledge base containing entities E and predicates Π, O = {E, Π}, where E = {e1, e2, . . . , ek} and Π = {π1, π2, . . . , πl}. Instantiation Function (I): A function that replaces placeholders in τ with entities and predicates from O, I : τ (σ(S)) × O → NL, where NL is the set of natural language sentences. Expert Mapping Function (µExpert): A function provided by a domain expert to map placeholders to appropriate ontology terms, µExpert : Placeholders → E ∪ Π. Knowledge Base (KB): A collection of instantiated syllogistic arguments, KB = {A1, A2, . . . , Am}, where Ai = {P ′ 1 , P′ 2 , . . . , P′ n , C′} and P ′ i , C′ are instantiated natural language sentences. Syllogistic Scheme (S): A logical inference pattern consisting of premises and a conclusion, S = {P1, P2, . . . , Pn, C}, where Pi is premise i and C is the conclusion. Syllogistic Scheme (S): A logical inference pattern consisting of premises and a conclusion, S = {P1, P2, . . . , Pn, C}, where Pi is premise i and C is the conclusion. Formal Argument Scheme (σ): Representation of a syllogistic scheme in first-order logic (FOL), σ(S) = {ϕ1, ϕ2, . . . , ϕn, ψ}, where ϕi corresponds to Pi and ψ corresponds to C. Formal Argument Scheme (σ): Representation of a syllogistic scheme in first-order logic (FOL), σ(S) = {ϕ1, ϕ2, . . . , ϕn, ψ}, where ϕi corresponds to Pi and ψ corresponds to C. Natural Language Template (τ ): A natural language schema mapping each formula in σ(S) to a sentence template, τ (σ(S)) = {τ1, τ2, . . . , τn, σ}, where τi is the sentence template for ϕi and σ is the sentence template for ψ. Natural Language Template (τ ): A natural language schema mapping each formula in σ(S) to a sentence template, τ (σ(S)) = {τ1, τ2, . . . , τn, σ}, where τi is the sentence template for ϕi and σ is the sentence template for ψ. Ontology (O): A domain-specific knowledge base containing entities E and predicates Π, O = {E, Π}, where E = {e1, e2, . . . , ek} and Π = {π1, π2, . . . , πl}. Ontology (O): A domain-specific knowledge base containing entities E and predicates Π, O = {E, Π}, where E = {e1, e2, . . . , ek} and Π = {π1, π2, . . . , πl}. Instantiation Function (I): A function that replaces placeholders in τ with entities and predicates from O, I : τ (σ(S)) × O → NL, where NL is the set of natural language sentences. Instantiation Function (I): A function that replaces placeholders in τ with entities and predicates from O, I : τ (σ(S)) × O → NL, where NL is the set of natural language sentences. Expert Mapping Function (µExpert): A function provided by a domain expert to map placeholders to appropriate ontology terms, µExpert : Placeholders → E ∪ Π. Expert Mapping Function (µExpert): A function provided by a domain expert to map placeholders to appropriate ontology terms, µExpert : Placeholders → E ∪ Π. Knowledge Base (KB): A collection of instantiated syllogistic arguments, KB = {A1, A2, . . . , Am}, where Ai = {P ′ 1 , P′ 2 , . . . , P′ n , C′} and P ′ i , C′ are instantiated natural language sentences. Knowledge Base (KB): A collection of instantiated syllogistic arguments, KB = {A1, A2, . . . , Am}, where Ai = {P ′ 1 , P′ 2 , . . . , P′ n , C′} and P ′ i , C′ are instantiated natural language sentences. A.1 Process Formalisation The process formalisation defines a systematic process for generating domain-specific syllogistic arguments by: 1. Defining formal representations of syllogistic schemes in first-order logic. Defining Generating natural language templates from these formal representations. Mapping placeholders to domain-specific entities and predicates using an ontology and expert knowledge. Instantiating the templates to produce logically valid and semantically sound arguments. Constructing a knowledge base for evaluating NLI models. Generating natural language templates from these formal representations. Generating natural language templates from these formal representations. Generating Mapping placeholders to domain-specific entities and predicates using an ontology and expert knowledge. Mapping placeholders to domain-specific entities and predicates using an ontology and expert knowledge. Mapping Instantiating the templates to produce logically valid and semantically sound arguments. Instantiating the templates to produce logically valid and semantically sound arguments. Instantiating Constructing a knowledge base for evaluating NLI models. Constructing a knowledge base for evaluating NLI models. Constructing This ensures that the generated arguments are both logically valid and contextually relevant to the biomedical domain. Input : A set of syllogistic schemes: S = {S1, S2, . . . , Sm}, an ontology: O = {E, Π}, an expert mapping function: µExpert. Input Output : A knowledge base of instantiated arguments: KB. Output Step 1 : Formal Argument Scheme Selection: For each syllogistic scheme Si ∈ S, define its formal argument scheme in first-order logic: Step 1 Step 2: Natural Language Template Generation : Transform each formula in σ(Si) into a natural language template: Step 2: Natural Language Template Generation Step 3: Ontology Mapping and Instantiation : Apply the expert mapping function to select appropriate entities and predicates from the ontology: Step 3: Ontology Mapping and Instantiation Instantiate the templates: under the following constraints: • Logical Validity : The instantiated arguments must preserve the logical structure of σ(Si). • Logical Validity • Domain Soundness: The selected entities and predicates must be semantically coherent within the targeted subdomain. • Domain Soundness: These constraints can be further formalised as: Logical Validity Constraint : The instantiated argument Ai must be logically valid: Logical Validity Constraint {ϕ ′ 1 , ϕ′ 2 , . . . , ϕ′ n} |= ψ ′ , where ϕ ′ j corresponds to the logical form of P ′ j . Domain Soundness Constraint: The entities and predicates used must be semantically valid within the domain: Domain Soundness Constraint: ∀e ∈ E ′ , π ∈ Π ′ , DomainValid(e, π) = True, where E′ ⊆ E and Π′ ⊆ Π are entities and predicates used in Ai Verification of Logical Validity : Ensure that the instantiated premises logically entail the conclusion: Verification of Logical Validity {ϕ ′ 1 , ϕ′ 2 , . . . , ϕ′ n} |= ψ ′ , using logical inference rules. Verification of Domain Soundness : Confirm that: Verification of Domain Soundness • All entities and predicates are correctly used. • There are no semantic contradictions. Step 4: Knowledge Base Construction : Aggregate all instantiated arguments into the knowledge base: Step 4: Knowledge Base Construction This is summarised with the following algorithmic outline: Authors: (1) Magdalena Wysocka, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom; (2) Danilo S. Carvalho, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom and Department of Computer Science, Univ. of Manchester, United Kingdom; (3) Oskar Wysocki, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom and ited Kingdom 3 I; (4) Marco Valentino, Idiap Research Institute, Switzerland; (5) André Freitas, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom, Department of Computer Science, Univ. of Manchester, United Kingdom and Idiap Research Institute, Switzerland. Authors: Authors: (1) Magdalena Wysocka, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom; (2) Danilo S. Carvalho, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom and Department of Computer Science, Univ. of Manchester, United Kingdom; (3) Oskar Wysocki, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom and ited Kingdom 3 I; (4) Marco Valentino, Idiap Research Institute, Switzerland; (5) André Freitas, National Biomarker Centre, CRUK-MI, Univ. of Manchester, United Kingdom, Department of Computer Science, Univ. of Manchester, United Kingdom and Idiap Research Institute, Switzerland. This paper is available on arxiv under CC BY-NC-SA 4.0 license. This paper is available on arxiv under CC BY-NC-SA 4.0 license. available on arxiv

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

A Formalization of the SylloBio-NLI Resource Generation Process

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

Accessing and Utilizing Pretrained LLMs: A Guide to Mistral AI and Other Open-Source Models"

New Study Reveals AI's Weak Spots in Medical Logic

How AI Models Handle Complex Biomedical Reasoning

How Effective Are AI Models at Biomedical Problem Solving?

Testing AI's Ability to Think Logically: A Breakthrough in Biomedical Research

Enhancing Syllogistic Reasoning in Biomedical NLI: Key Insights and Challenges

Accessing and Utilizing Pretrained LLMs: A Guide to Mistral AI and Other Open-Source Models"

New Study Reveals AI's Weak Spots in Medical Logic

How AI Models Handle Complex Biomedical Reasoning

How Effective Are AI Models at Biomedical Problem Solving?

Testing AI's Ability to Think Logically: A Breakthrough in Biomedical Research

Enhancing Syllogistic Reasoning in Biomedical NLI: Key Insights and Challenges

Light-Mode

Classic

Newspaper

Minty

Dark-Mode

Neon Noir

Minty

HN StartUps