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arxiv: 2604.19614 · v1 · submitted 2026-04-21 · 💻 cs.IT · math.IT

Recognition: unknown

Goal-Oriented Semantic Communication for Logical Decision Making

Ahmet Faruk Saz , Faramarz Fekri
Authors on Pith no claims yet

Pith reviewed 2026-05-10 01:17 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords goal-oriented semantic communicationfirst-order logicsemantic rate-distortioninformation bottlenecklogical decision makingautonomous agentsverifiable transmission
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The pith

A goal-oriented semantic system transmits only the first-order logic clauses most relevant to a decision task while preserving verifiability.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes a communication framework in which autonomous agents represent their shared world in first-order logic and then select which logical clauses to send based on how much each one reduces uncertainty about a higher-level decision goal. The selection rests on newly defined semantic entropy and mutual information quantities derived from an inductive probability measure over logic structures. A reader would care because raw sensor streams are too large for many wireless links, yet safety-critical choices such as path planning demand both low data volume and the ability to audit the reasoning afterward. The approach recasts rate-distortion optimization and the information bottleneck principle in semantic terms so that only decision-critical facts cross the channel. Demonstration occurs in a multi-agent urban simulator where agents must follow safe paths using deduction over the transmitted clauses.

Core claim

The paper claims that goal-oriented states, introduced as an abstraction layer over ordinary world states in a first-order logic hierarchy, allow a sender to rank and transmit only those FOL clauses that are most informative about the decision rules. Semantic entropy, conditional entropy, and mutual information are defined by assigning an inductive logical probability measure to the structures of the language; the resulting quantities support a semantic rate-distortion objective that minimizes communication cost subject to a bound on the remaining uncertainty about the goal states. Equivalently, the semantic information bottleneck principle extracts the same minimal sufficient set of clauses

What carries the argument

goal-oriented states as an abstraction layer over FOL world states, with transmission selected by the semantic information bottleneck that ranks clauses by their reduction in uncertainty about those states

If this is right

  • Only clauses critical to the goal states cross the channel, lowering required bandwidth compared with sending all observations.
  • The transmitted clauses remain inside the original FOL language, so any downstream deduction engine can verify consistency with safety rules.
  • The rate-distortion curve gives an explicit trade-off between bits sent and remaining uncertainty about the decision outcome.
  • Multiple agents can share the same logical representation and therefore coordinate without exchanging raw sensor data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same clause-ranking step could be inserted into existing logic-based planners to prune messages before transmission.
  • If the inductive probability measure can be learned from data rather than hand-specified, the framework might apply to domains where the full FOL theory is only partially known.
  • Scaling tests with increasing numbers of dynamic agents would reveal whether the computational cost of evaluating the semantic mutual information remains tractable.

Load-bearing premise

An inductive logical probability measure can be placed over semantic structures so that semantic entropy and mutual information become well-defined numbers usable inside a rate-distortion optimization.

What would settle it

In the urban simulator, replace the selected clauses with a random subset of equal size and check whether the receiver can still deduce the correct safe path; if deduction accuracy collapses or verification fails while data volume stays the same, the selection principle does not hold.

Figures

Figures reproduced from arXiv: 2604.19614 by Ahmet Faruk Saz, Faramarz Fekri.

Figure 1
Figure 1. Figure 1: Collaborative Perception in Autonomous Driving [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Driving Simulator Experiment Results of hypotheses evaluations that agree with the FI-baseline as a result of semantic communication. Action Decision Success Rate (A-DSR) is the fraction of time steps for which the decided action (Stop, Slow, Fast, or Normal) from semantic communication matches the FI-baseline. We compare the semantic selection strategy, minimiz￾ing (14), against a FOL-baseline that select… view at source ↗
read the original abstract

This paper develops a principled foundation for goal-oriented semantic communication for logical decision-making. Consider a setting where autonomous agents engage in collaborative perception. In such settings, the volume of sensory data and limited bandwidth often make transmission of raw observations infeasible, requiring intelligent selection of task-relevant information. Because these scenarios are safety-critical, the selection and decision processes must also be transparent and verifiable. To address this, we propose an explainable semantic communication framework grounded in a First-Order Logic (FOL) hierarchical representation of the world. We define semantic information, entropy, conditional entropy, and mutual information by assigning an inductive logical probability measure over semantic structures in the language. Based on these definitions, we formulate a goal-oriented semantic communication objective through semantic rate-distortion theory and, equivalently, through the semantic information bottleneck principle. In this framework, task rules are represented as goal-oriented states, defined as a layer over the world states to capture decision-relevant abstractions. The resulting principle selects evidence that is most informative about these states, aiming to transmit only those FOL clauses most critical for decision-making while preserving logical verifiability. We demonstrate the effectiveness of the approach in a deduction-based safe path-following task within an FOL-based urban environment simulator with multiple dynamic agents.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper develops a goal-oriented semantic communication framework for logical decision-making in collaborative perception settings among autonomous agents. It represents the world via a First-Order Logic (FOL) hierarchical structure, assigns an inductive logical probability measure over semantic structures to define semantic entropy, conditional entropy, and mutual information, and uses these to formulate a communication objective via semantic rate-distortion theory (equivalently, the semantic information bottleneck). Goal-oriented states capture decision-relevant abstractions over world states; the resulting principle selects and transmits only the most informative FOL clauses for the task while preserving logical verifiability. Effectiveness is shown via a deduction-based safe path-following demonstration in an FOL-based urban simulator with dynamic agents.

Significance. If the central construction holds, the work supplies a transparent, logically verifiable approach to semantic communication for safety-critical decision tasks, directly linking FOL reasoning with rate-distortion optimization. The implemented deduction-based simulator constitutes a concrete, reproducible testbed that demonstrates clause selection for a path-following objective; this is a strength for empirical grounding.

major comments (1)
  1. [§3] §3 (definitions of semantic entropy and mutual information): the inductive logical probability measure is introduced as the foundation for all information quantities and the subsequent rate-distortion objective, yet the manuscript provides no explicit construction, grounding, or computation procedure for assigning the measure to FOL structures in the simulator; without this, it is impossible to confirm that the measure is independent of the target task and that the objective does not reduce to a tautology.
minor comments (2)
  1. [Abstract and §5] The abstract states that the framework 'preserves logical verifiability' but does not specify which verification properties (e.g., soundness of the deduction engine or completeness of the transmitted clause set) are formally checked in the simulator; add a short paragraph or table entry clarifying this.
  2. [§2] Notation for goal-oriented states (introduced as a layer over world states) is used without an explicit mapping or example in the main text; a small illustrative diagram or set of clauses would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive summary, the recognition of the work's significance for safety-critical decision tasks, and the recommendation for minor revision. We address the single major comment point by point below.

read point-by-point responses

  1. Referee: [§3] §3 (definitions of semantic entropy and mutual information): the inductive logical probability measure is introduced as the foundation for all information quantities and the subsequent rate-distortion objective, yet the manuscript provides no explicit construction, grounding, or computation procedure for assigning the measure to FOL structures in the simulator; without this, it is impossible to confirm that the measure is independent of the target task and that the objective does not reduce to a tautology.

    Authors: We agree that the manuscript introduces the inductive logical probability measure in §3 as the foundation for the semantic entropy, mutual information, and rate-distortion objective but does not supply an explicit construction, grounding, or step-by-step computation procedure for its assignment to concrete FOL structures inside the simulator. This leaves open the questions of task-independence and whether the objective could become tautological. In the revised manuscript we will add a new subsection (placed after the simulator description) that (i) recalls the formal definition of the measure as a probability distribution over the set of models of the FOL language that is fixed by the language signature alone, (ii) states the independence from goal-oriented states by construction, and (iii) provides the concrete computation procedure used in the experiments (including how the measure is evaluated or approximated over the finite set of ground atoms and clauses generated by the urban simulator). We will also include a short numerical example with a handful of clauses to illustrate that the resulting semantic rate-distortion functional remains non-trivial. These additions will directly resolve the referee's concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper defines semantic entropy, conditional entropy, and mutual information by assigning an inductive logical probability measure over FOL semantic structures, then applies these definitions to formulate a goal-oriented rate-distortion objective and information-bottleneck principle for selecting task-critical clauses. This is a definitional step rather than a derivation that reduces to its own inputs by construction. The framework is evaluated via an implemented deduction-based simulator in an FOL urban environment with dynamic agents, supplying an independent empirical check on the path-following task. No equations or claims reduce a prediction to a fitted parameter, invoke self-citation for uniqueness, or smuggle an ansatz; the central construction remains self-contained against the provided definitions and demonstration.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the existence of a well-defined inductive logical probability measure over FOL structures and on the hierarchical separation of world states from goal-oriented states; these are not derived from first principles in the abstract.

axioms (2)
  • domain assumption First-order logic can hierarchically represent world states and decision-relevant abstractions
    Invoked when defining goal-oriented states as a layer over world states
  • ad hoc to paper An inductive logical probability measure exists and can be assigned to semantic structures
    Used to define semantic entropy, conditional entropy, and mutual information
invented entities (1)
  • Goal-oriented states no independent evidence
    purpose: Layer over world states to capture decision-relevant abstractions for the communication objective
    Introduced to formulate the semantic communication objective around task rules

pith-pipeline@v0.9.0 · 5514 in / 1379 out tokens · 24736 ms · 2026-05-10T01:17:48.289123+00:00 · methodology

discussion (0)

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Reference graph

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    Connection to Finite Mixture Models:In this interpre- tation, the constituentC w functions as a latent model index, p(C w)is a mixing weight, andp(e|C w)is a component- specific likelihood. The marginal likelihood of the evidence takes the standard finite-mixture form: p(e) = X w p(C w)p(e|C w) = X w πw fw(e), whereπ w =p(C w)andf w(e) =p(e|C w). Differen...

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    Model 4: Indicator Likelihood (Direct Uniformity):The simplest model treats evidence as exact logical evidence: p(e|C w) :=1{C w |=e}. Combined with the uniform priorp(C w) = 1/2K: p(C w |e) = 1{C w |=e} |C(e)| , p(e) = |C(e)| 2K , p(h|e) = |C(e∧h)| |C(e)| . This distinguishes only between evidence that is possible and evidence that is impossible under a ...

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    The Latent-Q Model as a Finite Mixture:For each observed evidence iteme t, introduce a latent variableZ t ∈ Q representing the underlying complete Q-sentence. The model has the standard finite-mixture architecture: p(et |C w) = |Q|X i=1 p(Zt =i|C w)| {z } mixing weight p(et |Z t =i, C w)| {z } emission probability . Herep(Z t =i|C w) =θ i(C w)is the proba...

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    Posterior Responsibilities:Theposterior responsibility of Q-sentenceQ i for explaining observatione t under con- stituentC w is: γ(w) t,i :=p(Z t =i|e t, Cw) = p(et |Q i)θ i(C w)P j p(et |Q j)θ j(C w) . This is directly analogous to the responsibilitiesγ ti =p(z t = i|x t, θ)in a Gaussian mixture model. It measures how much “credit” each hidden Q-sentence...

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    , θ(w) |Q| )are known, one can compute the posterior over constituents directly

    Expectation-Maximisation (EM) Procedure: When the constituent-conditioned Q-distributions θ(w) = (θ (w) 1 , . . . , θ(w) |Q| )are known, one can compute the posterior over constituents directly. However, when these distributions are unknown and must be estimated from data, the framework becomes a genuine EM algorithm: E-step.For each observatione t and ea...

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    Variational Approximation with Equal Splitting:When the full E-step posterior is intractable, one adopts a mean-field variational familyq(z) = Q ℓ qℓ(zℓ)and chooses a convenient q. Theequal-splittingheuristic sets: qℓ(i) =q(z ℓ =i|r ℓ =r) := Mri deg(r) ,deg(r) = KX j=1 Mrj , whereM ri ∈ {0,1}is the compatibility indicator (1 if Q- typeris compatible with ...

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    The Hierarchical Latent Model:A richer model intro- duces latent attributive constituents as an explicit layer: C w − →Ct j − →Q i − →e. The likelihood becomes: p(e|C w) = X j p(Ctj |C w) X i p(Qi |Ct j)p(e|Q i), with joint posterior responsibilities over both latent layers: p(Qi,Ct j |e, C w)∝p(e|Q i)p(Q i |Ct j)p(Ct j |C w). The Markov chain conditional...

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    Under the entity-block model with block weightsw u, distinct-predicate countsd u, and pairwise overlapso uv =|A u ∩A v|: R(e) = X u w2 u 2du + 2 X u<v wu wv 2|Au∩Av|

    Reduction to a Q-Level Tractable Score:The constituent-level second moment reduces exactly to a Q-level second moment via the enumeration structure: P C n(C) 2 = 2−M P q s(q) 2 +P q s(q)2 , wheres(q)is the Q-level weight andM=|Q|. Under the entity-block model with block weightsw u, distinct-predicate countsd u, and pairwise overlapso uv =|A u ∩A v|: R(e) ...

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    The sum is dominated byγ min, and optimisation reduces to a lexicographic comparison key over small integers(c, K,−H (1),

    Indicator-Likelihood Surrogate:Under Model 4, each per-hypothesis term reduces toF i ≈2 −γi whereγ i = 2|Q|−K −2 |Q|−K−H i. The sum is dominated byγ min, and optimisation reduces to a lexicographic comparison key over small integers(c, K,−H (1), . . .). This method is adopted in the present paper. G. Summary All models share the same logical language stru...