ARTIGO  
DOI: https://doi.org/10.21728/logeion.2026v12n2e-7959  
Data de submissão: 05/05/2026 Data de aprovação: 12/06/2026 Data de publicação: 19/06/2026  
A STRUCTURAL–PHILOSOPHICAL PERSPECTIVE ON  
COMPUTATION  
logic, mathematics and abstraction  
Lúcio Otávio Nunes1  
Orcid: https://orcid.org/0000-0003-3707-2633  
Universidade Federal dos Vales do Jequitinhonha e Mucuri  
lucio.otavio@ufvjm.edu.br  
______________________________  
Abstract  
This article offers a conceptual analysis of computation through three interdependent pillars: logic, mathematics,  
and abstraction. Logic provides formal constraints on symbolic manipulation; mathematics supplies  
interpretative structures and semantic resources; and abstraction enables the construction of models that  
represent and transform domains of interest. The method is philosophical and structural rather than technical,  
aiming to clarify how different foundational frameworks enable, shape, and delimit canonical notions of  
computation. The analysis is situated within the broader context of the philosophy of information, where  
computation is understood as a formal mechanism for representing and transforming informational structures.  
Historically, first-order logic played a paradigmatic role in early formal conceptions of rule-governed inference  
and symbolic representation, while contemporary computing draws on a broader family of logical foundations,  
including type-theoretic and categorical approaches. On this basis, the article argues that meaningful shifts in  
computational paradigms are best understood as revisions in one or more of these pillars, whether by adopting  
alternative logical systems, reconfiguring mathematical structures, or developing new modes of abstraction.  
Keywords: logic; mathematics; abstraction.  
UMA PERSPECTIVA ESTRUTURAL-FILOSÓFICA SOBRE COMPUTAÇÃO  
lógica, matemática e abstração  
Resumo  
Este artigo oferece uma análise conceitual da computação através de três pilares interdependentes: lógica,  
matemática e abstração. A lógica fornece restrições formais à manipulação simbólica; a matemática fornece  
estruturas interpretativas e recursos semânticos; e a abstração possibilita a construção de modelos que  
representam e transformam domínios de interesse. O método é filosófico e estrutural, em vez de técnico, visando  
esclarecer como diferentes estruturas fundamentais possibilitam, moldam e delimitam noções canônicas de  
computação. A análise está situada no contexto mais amplo da filosofia da informação, onde a computação é  
entendida como um mecanismo formal para representar e transformar estruturas informacionais. Historicamente,  
a lógica de primeira ordem desempenhou um papel paradigmático nas primeiras concepções formais de  
inferência regida por regras e representação simbólica, enquanto a computação contemporânea se baseia em uma  
família mais ampla de fundamentos lógicos, incluindo abordagens da teoria dos tipos e categóricas. Com base  
nisso, o artigo argumenta que mudanças significativas nos paradigmas computacionais são melhor  
compreendidas como revisões em um ou mais desses pilares, seja pela adoção de sistemas lógicos alternativos,  
pela reconfiguração de estruturas matemáticas ou pelo desenvolvimento de novos modos de abstração. Palavras-  
chave: lógica; matemática; abstração.  
Palavras-chave: lógica; matemática; abstração.  
1
Doutor em Química. Analista de Tecnologia da Informação na Universidade Federal dos Vales do  
Jequitinhonha e Mucuri - Campus JK.  
Esta obra está licenciada sob uma licença  
Creative Commons Attribution 4.0 International (CC BY-NC-SA 4.0).  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
 
ARTIGO  
UNA PERSPECTIVA ESTRUCTURAL-FILOSÓFICA SOBRE LA COMPUTACIÓN  
lógica, matemáticas y abstracción  
Resumen  
Este artículo ofrece un análisis conceptual de la computación a través de tres pilares interdependientes: lógica,  
matemáticas y abstracción. La lógica proporciona restricciones formales a la manipulación simbólica; las  
matemáticas aportan estructuras interpretativas y recursos semánticos; y la abstracción permite la construcción  
de modelos que representan y transforman dominios de interés. El método es filosófico y estructural, más que  
técnico, y busca clarificar cómo los diferentes marcos fundamentales posibilitan, configuran y delimitan las  
nociones canónicas de computación. El análisis se sitúa en el contexto más amplio de la filosofía de la  
información, donde la computación se entiende como un mecanismo formal para representar y transformar  
estructuras informacionales. Históricamente, la lógica de primer orden desempeñó un papel paradigmático en las  
primeras concepciones formales de la inferencia basada en reglas y la representación simbólica, mientras que la  
computación contemporánea se basa en una familia más amplia de fundamentos lógicos, incluyendo enfoques  
categóricos y de teoría de tipos. Partiendo de esta base, el artículo sostiene que los cambios significativos en los  
paradigmas computacionales se comprenden mejor como revisiones de uno o más de estos pilares, ya sea  
mediante la adopción de sistemas lógicos alternativos, la reconfiguración de estructuras matemáticas o el  
desarrollo de nuevos modos de abstracción.  
Palabras clave: lógica; matemáticas; abstracción.  
2
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
1 INTRODUCTION  
Languages can be understood as bridges between reality and the human mind, tools  
through which the brain transforms symbols referring to elements of the external world into  
structured mental representations. While all languages articulate relations between form and  
meaning, different symbolic systems represent reality in distinct ways (Boeckx, 2009). From  
this perspective, computation may be viewed, in a generalized sense, as a form of formal  
language capable of expressing abstract features of the world, particularly those amenable to  
mathematical modelling (Horst, 2011). In this sense, computation can also be interpreted as  
an informational process, in line with approaches developed in the philosophy of information  
(Floridi, 2002).  
Although computation can metaphorically be described as a language that expresses  
aspects of reality, it also possesses a precise technical meaning. In the classical sense,  
computation refers to the execution of an effective procedure: a finite, rule-governed process  
that transforms an input into an output when such an output is defined (Šekrst, 2025).  
Formally, computation consists in a stepwise symbolic transformation carried out under  
explicitly specified rules. This conception is canonically represented in the model of the  
Turing machine and in the broader Church–Turing framework, which articulates the notion of  
effective computability (Turing, 1936).  
3
Computation can be understood as resting upon three fundamental pillars: logic,  
mathematics, and abstraction. Logic provides the formal structure that underpins  
computational processes, much like the skeletal framework of a building. In this sense, logic  
may be interpreted as the syntactic dimension of computation: it governs the rules by which  
symbols are manipulated, thereby structuring the computational language itself (Shapiro,  
1995). Within such a framework, computation can be described as a process in which an input  
is transformed, through formally specified procedures, into an output. Logic thus constitutes a  
structural core of computational systems (Yamada, 2023).  
Mathematics, in turn, supplies the semantic dimension. It provides the abstract entities,  
relations, and transformations that give content to what logic structures. If logic corresponds  
to syntax, mathematics corresponds to semantics, the domain of meaning that interprets  
symbolic manipulation (Goldfarb; Osborn et al. 1970). Continuing the architectural analogy,  
if logic forms the structural framework, mathematics provides the conceptual design that  
renders the structure intelligible (O'Regan, 2013).  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
The interplay between logic and mathematics enables the development of  
computational models. Logic serves as the formal mechanism of representation, while  
mathematics provides the interpretative framework that gives the model its content (Avigad,  
2022). This synthesis results in what we call abstraction, an essential process in modern  
computing. Abstractions such as algorithms encapsulate logical operations and mathematical  
concepts in a unified structure, allowing complex phenomena to be modelled and manipulated  
effectively (Carette; Farmer, 2019).  
Historically, first-order logic played a central role in shaping early formal conceptions  
of computation by providing a precise syntactic framework with well-defined semantic  
interpretation (Abiteboul; Vianu, 1995). However, the theoretical foundations of  
contemporary computing extend beyond first-order logic. Developments in type theory,  
lambda calculus, and category-theoretic approaches have significantly expanded the formal  
tools available for representing computational structures (Pierce, 2002; Huth; Ryan, 2004). In  
this sense, first-order logic may be regarded as a paradigmatic starting point rather than as the  
exclusive foundation of computation.  
4
A further philosophical implication of this framework concerns its epistemic role.  
Logic, mathematics, and abstraction are not merely structural components of computation;  
they function as formal resources through which models and representations are constructed  
in order to interpret and explain aspects of reality (Vámos, 1991). When employed in formal  
methods, these pillars operate as epistemic tools: they mediate between symbolic structures  
and the domains they are intended to represent. At the same time, they also delineate the  
limits of classical computation, insofar as the scope of what can be modelled or expressed  
depends on the logical systems, mathematical structures, and modes of abstraction adopted. In  
this sense, computation is not only a technical practice but also an epistemological pathway  
shaped by its foundational architecture (Sloman, 1982).  
In this broader perspective, computation can be analysed philosophically as a formal  
language describing structured aspects of reality, and technologically as a system through  
which humans manipulate formal structures to model and transform phenomena (Brey;  
Søraker, 2009). This article examines how logic and mathematics both structure and delimit  
computation, and article opens the discussion of how alternative logical frameworks,  
mathematical structures, or modes of abstraction may reshape its conceptual boundaries.  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
2 LOGIC AS A FORMAL STRUCTURE  
As suggested above, logic functions as a structural framework for computation. In its  
historical development, first-order logic provided one of the earliest systematic formal  
systems capable of expressing general rules of inference with precise syntactic and semantic  
coordination. For this reason, it became deeply influential in early formalizations of  
computability (Davis, 1993).  
First-order logic offers a powerful mechanism for expressing regularities and formal  
inference within a finite symbolic system. Its inference rules ensure that deduction proceeds  
in a stepwise and determinate manner, an aspect that mirrors the finitary character of classical  
computation (Ewald, 2018). In this historical sense, first-order logic served as a foundational  
paradigm for understanding how formal symbolic manipulation could be rigorously structured  
(Barwise, 1977).  
Among the central meta-theoretical properties of first-order logic are completeness  
and compactness. The completeness theorem establishes a precise correspondence between  
semantic validity and formal provability: a formula is valid in all models if and only if it is  
derivable within the deductive system (Barwise, 1977). This alignment between syntax and  
semantics provided a powerful conceptual model for understanding formal symbolic systems.  
In early reflections on computation, such harmony reinforced the view that rule-governed  
symbolic manipulation could reliably capture meaningful transformations, an idea that later  
became central to computability theory. The compactness theorem, on the other hand,  
expresses a structural principle concerning finitary reasoning: if every finite subset of a set of  
formulas is satisfiable, then the entire set is satisfiable. Although compactness does not  
impose finiteness on the domains under consideration, since first-order logic freely admits  
infinite models, it reflects the fundamentally finitary character of formal deduction (Dawson  
Jr, 1993). Logical consequence in first-order logic is determined through finite derivations,  
and this finitary aspect parallels the stepwise nature of classical computation, in which  
effective procedures operate through discrete, finite transitions. While completeness and  
compactness do not themselves define computation, they contributed to shaping the  
intellectual environment in which computability was conceptualized: a framework in which  
formal systems were understood as rule-governed, finitely articulated structures capable of  
expressing meaningful relations over potentially infinite domains (Enderton, 2001).  
However, contemporary computational theory relies on a broader understanding of  
logic. Type theory, for instance, provides a refined framework for classifying expressions and  
5
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
ensuring consistency through structured typing systems. Through the Curry–Howard  
correspondence, logical propositions are interpreted as types and proofs as programs,  
establishing a deep connection between logic and computation. Such developments underpin  
modern functional programming languages, including those based on the Hindley–Milner  
type system, as exemplified in languages such as Haskell (Milner, 1978; Pierce, 2002). These  
advances demonstrate that the logical foundations of computation have evolved significantly  
beyond first-order logic, incorporating richer structural mechanisms for representing  
algorithms and programs.  
3 MATHEMATICS AS SEMANTICS  
If we consider the computational process as mechanical, logic may be viewed as the  
structural framework, and computation as the movement. However, without order, this  
movement lacks direction or meaning (Scott; Strachey 1971). This is precisely where  
mathematics enters. As the semantic layer of computation, mathematics provides order and  
purpose to the mechanical process governed by logic. Within this context, two mathematical  
structures are intrinsic to computation: sets and functions, which together define what it  
means to compute (Manzano, 1996).  
6
Sets are essential for delimiting elements: they structure the collection of propositions  
in logic, the domain of arithmetic objects, the sequence of steps in a procedure, or the  
alphabet of symbols in a formal language. This illustrates the foundational role of set theory  
in computation (Devlin, 2018). On the other hand, functions lie at the heart of computational  
operations. Through functions, mathematical objects are transformed: numbers are combined  
to produce results, inputs are mapped to outputs, and abstract processes are executed.  
Functions thus act upon sets to drive computation forward. In this way, set theory and  
function theory provide the semantic foundation that gives meaning to the formal language of  
logic (Van Heijenoort, 1977; Manzano, 1996).  
Peano Arithmetic serves as a bridge between logic and mathematics. This theory does  
not claim that logic captures the essence of numbers, but rather that it provides a formal  
description through which numbers can be recognized and manipulated. In this framework,  
natural numbers are not discovered by logic, but described in a way that makes them  
accessible to formal reasoning (Kaye, 1991). Once numbers are logically recognizable, they  
become manipulable through logical inference, precisely what occurs in computation. It is  
important to note, however, that Peano Arithmetic is ultimately constrained by the same  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
limitations that affect formal logic. As such, it cannot fully express the totality of number  
theory, particularly in light of incompleteness results (Smith, 2013).  
A crucial aspect of Peano Arithmetic is its use of induction, which enables logic to  
express properties of natural numbers (Jongsma, 2019). Induction transforms the infinite  
structure of the natural numbers, so essential to computation, into something countable and  
tractable within a formal system. By introducing a stepwise structure over this infinite set,  
induction allows logic, which is inherently finite, to reason about infinity. It is through  
induction that a finite formal language becomes capable of expressing general truths over an  
infinite domain. This mechanism is fundamental for computation, as it permits the encoding  
of recursive definitions and iterative procedures within a logical framework (Parsons, 1990).  
The Turing machine summarizes the deep relationship between logic and  
mathematics, between syntax and semantics (Weisstein, 2002). It is, so to speak, the concrete  
embodiment of more fundamental concepts such as Peano Arithmetic, which itself emerges  
from the interplay between formal logic and mathematical abstraction. The Turing machine is  
not merely a technical artifact, but a conceptual synthesis: a mechanism that formalizes  
deduction, number manipulation, and abstract computation in a single coherent system  
(Copeland, 1997; Shagrir, 2006).  
7
4 ABSTRACTION: THE FLEXIBILITY OF COMPUTATION  
Since logic provides the syntax and mathematics the semantics, the process of  
abstraction gives form and expressive power to computation. Through generalization,  
abstraction allows the rules of logic and the symbols of mathematics to say something about  
real or imagined processes (Colburn; Shute, 2007). In this sense, abstraction can be likened to  
a literary composition written in a specific language, in this case, computation. Logic provides  
the syntactic structure of this language, and mathematics provides its interpretative meaning.  
Abstraction, then, is what makes computation both flexible and creative: it shapes models that  
go beyond pure formalism to approximate real structures or processes (Colburn; Shute, 2007).  
If we view a computational system as a literary work, various models of computation  
may be seen as distinct creative artifacts shaped by human ingenuity. Turing machines,  
automata, and artificial neural networks are all formal systems that emerge from the abstract  
flexibility of computation (Forcada, 2002). Each of these models is governed by its own  
formal language, much like dialects of a broader computational language. In this context, the  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
boundary between a real-world problem and its computational solution is often nothing more  
than a matter of human creativity (Rapaport, 2020).  
Computation can therefore be viewed as a general language through which we speak  
about the world. Although it does not access reality directly, it constructs approximate models  
of phenomena that appear real to us. At the same time, computation functions as a  
technological tool that allows humans to act upon nature, much like early humans shaped  
stones to hunt. In this way, abstraction not only expands the descriptive power of logic and  
mathematics, but also mediates between symbolic reasoning and practical engagement with  
the world (Floridi, 2002).  
Since computation can be viewed as a language that captures certain aspects of reality,  
it follows that some computational languages may have more or less expressive power. This  
opens up the possibility of enhancing the power of computation by modifying its foundational  
components. One potential avenue lies in altering the underlying logic. First computational  
models rely on first-order logic, a system known for its robustness and objectivity. While  
first-order logic is remarkably effective for formal reasoning, it has limited capacity to  
express rich semantic structures. It is therefore natural to consider whether a more expressive  
logical framework might lead to computational improvements. However, the challenge lies in  
finding a system that has semantic flexibility without sacrificing precision, determinacy, and  
objectivity (Shapiro, 2014).  
8
Another strategy would be to revise the mathematical structures used in computation.  
Much of classical computation relies on set theory and functions. These could be replaced, or  
at least supplemented, by alternative frameworks, such as topological spaces or algebraic  
systems (Buchberger; Collins et al. 1982). A particularly promising direction is the  
application of category theory, which offers a high level of abstraction and unification across  
different areas of mathematics. However, identifying alternative mathematical structures  
suitable for computation is a non-trivial task and may require years of foundational research  
before becoming practically applicable (Awodey, 2010).  
A third and perhaps more immediate possibility lies in the domain of abstraction itself.  
Due to its flexibility, abstraction may offer the most accessible path for enhancing  
computational capabilities. This does not imply that breakthroughs are easily achieved, but it  
does suggest that we already possess robust systems, such as Turing machines, upon which  
new layers of abstraction can be developed. This infrastructure saves the effort of rebuilding  
formal foundations from scratch and allows researchers to focus directly on refining abstract  
models. Abstraction may therefore hold the key to solving major computational challenges,  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
including the famed P vs NP problem (Cook, 2000). Ultimately, however, progress along any  
of these paths depends on sustained and rigorous research (MacLennan, 2004).  
5 GOING FURTHER: THE CLASSICAL MODEL  
We have now reached a point where it is possible to observe the fundamental role of  
induction and recursion in the current computational paradigm. These two concepts are  
deeply interconnected within theoretical computer science: while induction enables logic to  
articulate properties of infinite domains such as the natural numbers, recursion provides a  
formal mechanism for defining effective operations over such domains. Together, they serve  
as central structural elements in classical models of computation, and without them the  
standard conception of computation, as formalized in the Church–Turing framework, would  
not have emerged. However, recognizing their centrality also opens a conceptual window  
onto the broader landscape of computational formalisms (Soare, 1996).  
Rather than suggesting that induction or recursion can be “improved” in a simple or  
unilateral sense, it is more precise to frame the inquiry in terms of extensions and variants of  
the classical model. Over the past decades, a number of theoretical frameworks have been  
proposed that extend or reinterpret aspects of classical computability. One such line of  
thought involves hypercomputation, which explores formal models that, under idealized  
assumptions, transcend the limits of Turing computability by employing oracles or non-  
standard transitions. While hypercomputational models remain hypothetical and contested,  
they illustrate how foundational assumptions about effective procedures influence what is  
considered computable (Ord, 2006).  
9
Other extensions arise within practical and theoretical domains that enrich the classical  
paradigm. Concurrent and interactive models of computation, for example, foreground  
ongoing interaction with an environment rather than a closed, one-shot input–output  
transformation, challenging certain assumptions about halting and isolation in standard  
models. Quantum computing exemplifies another paradigm in which the basic primitives of  
state and transformation differ from classical computation, even if many quantum algorithms  
are interpretable within Turing-equivalent frameworks (Steane, 1998).  
A further extension is found in coinductive methods, which provide a formal apparatus  
for reasoning about potentially infinite structures and processes by means of observations and  
corecursive definitions. Coinduction thereby expands the expressive scope for representing  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
and reasoning about infinite behaviour without presupposing classical induction (Wegner;  
Goldin, 1999).  
Crucially, though these approaches differ in motivation and formal structure, they  
remain deeply anchored in the conceptual pillars outlined above, whether by modifying the  
logical formalism (e.g., interactive or concurrent logics), by enriching the underlying  
mathematical structures (e.g., vector spaces in quantum computing), or by elaborating modes  
of abstraction. For this reason, understanding the classical pillars of computation continues to  
be essential: any serious attempt to extend or reinterpret the computational paradigm must do  
so with full awareness of these foundations so that such extensions remain coherent,  
grounded, and meaningful (Turner, 2021; Zach, 2024).  
6 CONCLUSION  
This article has explored how the initial computation models rest upon some  
interdependent pillars: logic, mathematics, and abstraction. Each plays a distinct role, logic  
provides the structural syntax, mathematics supplies the semantic content, and abstraction  
enables meaningful expression through formal systems. Together, they form a conceptual  
framework that both enables and limits computation the first computation models.  
Recognizing these pillars clarifies not only the structure of current computational  
models, but also the boundaries they impose. The expressive capacity of computation is  
ultimately constrained by the formal tools it employs. However, as shown here, any  
substantial advance, whether philosophical, theoretical, or technological, must pass through a  
critical re-examination of these elements. Whether through modifications to logic, alternative  
mathematical frameworks, or novel forms of abstraction, new paradigms of computation will  
emerge only through a deeper understanding of its foundations.  
10  
In this sense, computation can be viewed not merely as a technical process, but as a  
formal language shaped by its internal architecture. To explore the future of computation is  
thus to reflect on its logical and mathematical essence, and to envision how this language  
might evolve to express new realities.  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
REFERENCES  
ABITEBOUL, S.; VIANU, V. Computing with first-order logic. Journal of Computer and  
System Sciences, v. 50, n. 2, p. 309–335, 1995.  
AVIGAD, J. Mathematical logic and computation. Cambridge: Cambridge University  
Press, 2022.  
AWODEY, S. Category theory. Oxford: Oxford University Press, 2010.  
BARWISE, J. An introduction to first-order logic. In: BARWISE, J. Studies in Logic and  
the Foundations of Mathematics. Amsterdam: Elsevier, 1977. v. 90, p. 5–46.  
BOECKX, C. Language in cognition: uncovering mental structures and the rules behind  
them. Hoboken: John Wiley & Sons, 2009.  
BREY, P.; SØRAKER, J. H. Philosophy of computing and information technology. In:  
MEIJERS, A. (ed.). Philosophy of technology and engineering sciences. Amsterdam:  
Elsevier, 2009. p. 1341–1407.  
BUCHBERGER, B. et al. Computer algebra symbolic and algebraic computation. ACM  
SIGSAM Bulletin, v. 16, n. 4, p. 5, 1982.  
11  
CARETTE, J.; FARMER, W. M. Towards specifying symbolic computation. In:  
INTELLIGENT COMPUTER MATHEMATICS (CICM 2019), 12., 2019. Cham.  
Proceedings [...]. Cham: Springer, 2019. p. 12.  
COLBURN, T.; SHUTE, G. Abstraction in computer science. Minds and Machines, v. 17, n.  
2, p. 169–184, 2007.  
COOK, S. The P versus NP problem. Clay Mathematics Institute, v. 2, n. 6, p. 3, 2000.  
COPELAND, B. J. The Church-Turing Thesis. The Stanford Encyclopedia of Philosophy  
(Spring 2026 Edition). ZALTA, E. N.; NODELMAN, U. (eds.). Available from:  
https://plato.stanford.edu/archives/spr2026/entries/church-turing/. Access in: 12 May 2026.  
DAVIS, M. First order logic. In: GABBAY, D. M.; HOGGER, C. J.; ROBINSON, J.;  
SIEKMANN, J. (ed.). Handbook of logic in artificial intelligence and logic programming.  
1993. v. 1, p. 31–65.  
DAWSON JR., J. W. The compactness of first-order logic: from Gödel to Lindström. History  
and Philosophy of Logic, v. 14, n. 1, p. 15–37, 1993.  
DEVLIN, K. Sets, functions, and logic: an introduction to abstract mathematics. Boca  
Raton: Chapman and Hall/CRC, 2018.  
ENDERTON, H. B. A mathematical introduction to logic. Amsterdam: Elsevier, 2001.  
EWALD, W. The emergence of first-order logic. The Stanford Encyclopedia of Philosophy  
(Spring 2019 Edition). ZALTA, E. N.; NODELMAN, U. (ed.). Available from:  
https://plato.stanford.edu/archives/spr2019/entries/logic-firstorder-emergence. Access in: 12  
May 2026.  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
FLORIDI, L. What is the philosophy of information? Metaphilosophy, v. 33, n. 1-2, p. 123–  
145, 2002.  
FORCADA, M. L. Neural networks: automata and formal models of computation: an  
unfinished survey. Alacant: Universitat d’Alacant, 2002. Available from:  
https://www.dlsi.ua.es/~mlf/nnafmc/pbook.pdf. Access in: 12 May 2026.  
GOLDFARB, D. et al. Mathematics of computation. American Mathematical Society, v.  
24, p. 23, 1970.  
HORST, S. Symbols, computation, and intentionality. Cambridge: MIT Press, 2011.  
HUTH, M.; RYAN, M. Logic in computer science: modelling and reasoning about systems.  
Cambridge: Cambridge University Press, 2004.  
JONGSMA, C. Mathematical induction and arithmetic. In: JONGSMA, C. Introduction to  
discrete mathematics via logic and proof. Cham: Springer, 2019. p. 149–204.  
KAYE, R. Models of Peano arithmetic. Oxford: Oxford University Press, 1991.  
MACLENNAN, B. J. Natural computation and non-Turing models of computation.  
Theoretical Computer Science, v. 317, n. 1-3, p. 115–145, 2004.  
12  
MANZANO, M. Extensions of first-order logic. Cambridge: Cambridge University Press,  
1996.  
MILNER, R. A theory of type polymorphism in programming. Journal of Computer and  
System Sciences, v. 17, n. 3, p. 348–375, 1978.  
O’REGAN, G. Mathematics in computing. Cham: Springer, 2013.  
ORD, T. The many forms of hypercomputation. Applied Mathematics and Computation, v.  
178, n. 1, p. 143–153, 2006.  
PARSONS, C. The structuralist view of mathematical objects. Synthese, v. 84, p. 303–346,  
1990.  
PIERCE, B. C. Types and programming languages. Cambridge: MIT Press, 2002.  
RAPAPORT, W. J. Philosophy of computer science. Buffalo: University at Buffalo, 2020.  
SCOTT, D. S.; STRACHEY, C. Toward a mathematical semantics for computer  
languages. Oxford: Oxford University Computing Laboratory, 1971.  
ŠEKRST, K. Computation. In: ŠEKRST, K. The illusion engine: the quest for machine  
consciousness. Cham: Springer, 2025. p. 105–121.  
SHAGRIR, O. Gödel on Turing on computability. In: OLSZEWSKI, A.; WOLENSKI, J.;  
JANUSZ, R. (ed.). Church’s Thesis after 70. Frankfurt: Ontos Verlag, 2006. p. 393–419.  
SHAPIRO, S. Reasoning, logic and computation. Philosophia Mathematica, v. 3, n. 1, p.  
31–51, 1995.  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.  
ARTIGO  
SHAPIRO, S. Varieties of logic. Oxford: Oxford University Press, 2014.  
SLOMAN, A. Computational epistemology. Sussex: University of Sussex, 1982.  
SMITH, P. An introduction to Gödel’s theorems. Cambridge: Cambridge University Press,  
2013.  
SOARE, R. I. Computability and recursion. Bulletin of Symbolic Logic, v. 2, n. 3, p. 284–  
321, 1996.  
STEANE, A. Quantum computing. Reports on Progress in Physics, v. 61, n. 2, p. 117–173,  
1998.  
TURING, A. M. On computable numbers, with an application to the Entscheidungsproblem.  
Proceedings of the London Mathematical Society, v. 2, n. 42, p. 230–265, 1936.  
TURNER, R. Computational abstraction. Entropy, v. 23, n. 2, p. 213, 2021.  
VÁMOS, T. Computer epistemology. Singapore: World Scientific, 1991.  
VAN HEIJENOORT, J. Set-theoretic semantics. In: GANDY, R. O.; HYLAND, J. M. E.  
(ed.). Studies in Logic and the Foundations of Mathematics. Amsterdam: Elsevier, 1977.  
v. 87, p. 183–190.  
13  
WEGNER, P.; GOLDIN, D. Coinductive models of finite computing agents. Electronic  
Notes in Theoretical Computer Science, v. 19, p. 81–101, 1999.  
WEISSTEIN, E. W. Turing machine. 2002. Available from:  
https://mathworld.wolfram.com/TuringMachine.html. Access in: 12 May 2026.  
YAMADA, N. Logic and computation as combinatorics. arXiv preprint, arXiv:2306.07806,  
2023.  
ZACH, R. Logic in mathematics and computer science. arXiv preprint, arXiv:2404.09033,  
2024.  
LOGEION: Filosofia da informação, Rio de Janeiro, v. 12, n. 2, p. 1-13, e-7959, jan./jun. 2026.