Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Mimamsa Inspired Framework For Instruction Sequencing In AI Agents

Bama Srinivasan

TL;DR

The paper addresses the problem of reliable instruction sequencing for AI agents, focusing on temporal reasoning and object–state dependencies. It introduces a Mimāṁsā-inspired framework that treats instructions as action–object pairs and formalizes three sequencing paradigms: Direct Assertion, Purpose-Based, and Iterative Procedure, all grounded in a formal action–object imperative logic. Core contributions include modeling action–object dependencies, formalizing sequencing rules (OCS and PLS), and proving a Validity Theorem along with soundness and completeness. The work enables principled, verifiable sequencing suitable for planning and robotics, with practical realization via a MIRA AI Agent for real-time validation.

Abstract

This paper presents a formal framework for sequencing instructions in AI agents, inspired by the Indian philosophical system of Mimamsa. The framework formalizes sequencing mechanisms through action object pairs in three distinct ways: direct assertion (Srutikrama) for temporal precedence, purpose driven sequencing (Arthakrama) for functional dependencies, and iterative procedures (Pravrittikrama) for distinguishing between parallel and sequential execution in repetitive tasks. It introduces the syntax and semantics of an action object imperative logic, extending the MIRA formalism (Srinivasan and Parthasarathi, 2021) with explicit deduction rules for sequencing. The correctness of instruction sequencing is established through a validated theorem, which is based on object dependencies across successive instructions. This is further supported by proofs of soundness and completeness. This formal verification enables reliable instruction sequencing, impacting AI applications across areas like task planning and robotics by addressing temporal reasoning and dependency modeling.

A Mimamsa Inspired Framework For Instruction Sequencing In AI Agents

TL;DR

The paper addresses the problem of reliable instruction sequencing for AI agents, focusing on temporal reasoning and object–state dependencies. It introduces a Mimāṁsā-inspired framework that treats instructions as action–object pairs and formalizes three sequencing paradigms: Direct Assertion, Purpose-Based, and Iterative Procedure, all grounded in a formal action–object imperative logic. Core contributions include modeling action–object dependencies, formalizing sequencing rules (OCS and PLS), and proving a Validity Theorem along with soundness and completeness. The work enables principled, verifiable sequencing suitable for planning and robotics, with practical realization via a MIRA AI Agent for real-time validation.

Abstract

This paper presents a formal framework for sequencing instructions in AI agents, inspired by the Indian philosophical system of Mimamsa. The framework formalizes sequencing mechanisms through action object pairs in three distinct ways: direct assertion (Srutikrama) for temporal precedence, purpose driven sequencing (Arthakrama) for functional dependencies, and iterative procedures (Pravrittikrama) for distinguishing between parallel and sequential execution in repetitive tasks. It introduces the syntax and semantics of an action object imperative logic, extending the MIRA formalism (Srinivasan and Parthasarathi, 2021) with explicit deduction rules for sequencing. The correctness of instruction sequencing is established through a validated theorem, which is based on object dependencies across successive instructions. This is further supported by proofs of soundness and completeness. This formal verification enables reliable instruction sequencing, impacting AI applications across areas like task planning and robotics by addressing temporal reasoning and dependency modeling.
Paper Structure (23 sections, 3 theorems, 20 equations, 1 table)

This paper contains 23 sections, 3 theorems, 20 equations, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Extension of Syntax and Semantics for Action-Object Imperative Logic
  4. Syntax
  5. Semantics
  6. Sequencing Methods
  7. Direct Assertion (Śrutikrama)
  8. Sequencing based on purpose
  9. Sequential and Parallel Execution Methods for Repetitive Tasks
  10. Sequential Completion Method
  11. Step-by-Step Parallel Method (Iterative Procedure)
  12. Object Dependency and Functional Dependency in Instruction Sequencing
  13. Object Dependency Condition
  14. Functional Dependency Condition
  15. Validity Theorem for Sequencing
  16. ...and 8 more sections

Key Result

Theorem 5.3

Validity of Instruction Sequence with Object and Functional Dependencies Let $I = \{i_1, i_2, \ldots, i_n\}$ be a sequence of instructions with $i_j = (a_j, O_j)$. The sequence is valid if: then: where $D(i_j, i_{j+1})$ expresses a dependency between $i_j$ and $i_{j+1}$.

Theorems & Definitions (8)

  • Definition 5.1
  • Definition 5.2
  • Theorem 5.3
  • proof
  • Theorem 6.1
  • proof
  • Theorem 6.2
  • proof