We present a mathematical approach to defeasible reasoning based on arguments. This approach integrates the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. The main contribution of this paper is a precise, well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. It aims for usability rather than novelty. We prove that an order relation can be introduced among equivalence classes of arguments under the equi-specificity relation. We also prove (...) a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search space for checking specificity. In order to implement the theoretical ideas, the language is restricted to Horn clauses for the evidential context. The language used to represent defeasible rules has been restricted in a similar way. The authors intend this work to unify the various existing approaches to argument-based defeasible reasoning. (shrink)

Over the past decade or so, a new interdisciplinary field has emerged in the ground between, on the one hand, computer science – and artificial intelligence in particular – and, on the other, the area of philosophy concentrating on the language and structure of argument. There are now hundreds of researchers worldwide who would consider themselves a part of this nascent community. Various terms have been proposed for the area, including "Computational Dialectics," "Argumentation Technology," and "Argument-based Computing," but the term (...) that has stuck is simply Argument & Computation. It encompasses several specific strands of research, such as: . the use of theories of argument, and dialectic in particular, in the design and implementation of protocols for multi-agent action and communication; . the application of theories of argument and rhetoric in natural language processing and affective computing; . the use of argument-based structures for autonomous reasoning in artificial intelligence, and in particular, for defeasible reasoning; . computer-supported collaborative argumentation – the implementation of software tools for enabling online argument in domains such as education and e-government. These strands come together to form the core of a research field that covers parts of artificial intelligence (AI), philosophy, linguistics, and cognitive science, but, increasingly, is building an identity of its own. (shrink)

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyze their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. LogicProgrammingisacomputationalparadigmthathasproducedcompu- tationallyattractivesystemswithremarkablesuccessinmanyapplications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation engine (...) to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use in applications. (shrink)

In this paper we propose an approach to multi-source belief revision where the trust or credibility assigned to informant agents can be revised. In our proposal, the credibility of each informant represented as a strict partial order among informant agents, will be maintained in a repository called credibility base. Upon arrival of new information concerning the credibility of its peers, an agent will be capable of revising this strict partial order, changing the trust assigned to its peers accordingly. Our goal (...) is to formalize a set of change operators over the credibility base: expansion, contraction, prioritized, and non-prioritized revision. These operators will provide the capability of dynamically modifying the credibility of informants considering the reliability of the information. This dynamics will reflect a new perception of trust assigned to the informant, or extend the set of informants by admitting the addition of new informant agents. (shrink)

This work formalizes an informant-based structured argumentation approach in a multi-agent setting, where the knowledge base of an agent may include information provided by other agents, and each piece of knowledge comes attached with its informant. In that way, arguments are associated with the set of informants corresponding to the information they are built upon. Our approach proposes an informant-based notion of argument strength, where the strength of an argument is determined by the credibility of its informant agents. Moreover, we (...) consider that the strength of an argument is not absolute, but it is relative to the resolution of the conflicts the argument is involved in. In other words, the strength of an argument may vary from one context to another, as it will be determined by comparison to its attacking arguments (respectively, the arguments it attacks). Finally, we equip agents with the means to express reasons for or against the consideration of any piece of information provided by a given informant agent. Consequently, we allow agents to argue about the arguments’ strength through the construction of arguments that challenge (respectively, defeat) or are in favour of their informant agents. (shrink)

This work introduces the Attack-Support Argumentation Framework (ASAF), an approach to abstract argumentation that allows for the representation and combination of attack and support relations. This framework extends the argumentation Framework with Recursive Attacks (AFRA) in two ways. Firstly, it adds a support relation enabling to express support for arguments; this support can also be given to attacks, and to the support relation itself. Secondly, it extends AFRA’s attack relation by allowing attacks to the aforementioned support relation. Moreover, since the (...) support relation of the ASAF has a necessity interpretation, the ASAF also extends the Argumentation Framework with Necessities (AFN). Thus, the ASAF provides a unified framework for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level. (shrink)

Argumentation is a form of reasoning where a claim is accepted or rejected according to the analysis of the arguments for and against it; furthermore, it provides a reasoning mechanism able to handle contradictory, incomplete and uncertain information in real-world situations. We combine Bipolar Argumentation Frameworks (an extension of Dung’s work) with an Algebra of Argumentation Labels modeling two independent types of interaction between arguments, representing meta-information associated with arguments, and introducing an acceptability notion that will give more information for (...) arguments acceptability. (shrink)

Structured argumentation systems, and their implementation, represent an important research subject in the area of Knowledge Representation and Reasoning. Structured argumentation advances over abstract argumentation frameworks by providing the internal construction of the arguments that are usually defined by a set of (strict and defeasible) rules. By considering the structure of arguments, it becomes possible to analyze reasons for and against a conclusion, and the warrant status of such a claim in the context of a knowledge base represents the main (...) output of a dialectical process. Computing such statuses is a costly process, and any update to the knowledge base could potentially have a huge impact if done naively. In this work, we investigate the case of updates consisting of both additions and removals of pieces of knowledge in the Defeasible Logic Programming (DeLP) framework, first analyzing the complexity of the problem and then identifying conditions under which we can avoid unnecessary computations—central to this is the development of structures (e.g. graphs) to keep track of which results can potentially be affected by a given update. We introduce a technique for the incremental computation of the warrant statuses of conclusions in DeLP knowledge bases that evolve due to the application of (sets of) updates. We present the results of a thorough experimental evaluation showing that our incremental approach yields significantly faster running times in practice, as well as overall fewer recomputations, even in the case of sets of updates performed simultaneously. (shrink)

This paper proposes the use of an argumentation framework with recursive attacks to address a trust model in a collaborative open multi-agent system. Our approach is focused on scenarios where agents share information about the credibility (informational trust) they have assigned to their peers. We will represent informants’ credibility through credibility objects which will include not only trust information but also the informant source. This leads to a recursive setting where the reliability of certain credibility information depends on the credibility (...) of other pieces of information that should be subject to the same analysis. Credibility objects are maintained in a credibility base which can have information in conflict. In this scenario, we will formally show that our proposal will produce a partially ordered credibility relation; such relation contains the information that can be justified by an argumentation process. (shrink)

The problem of knowledge evolution has received considerable attention over the years. Mainly, the study of the dynamics of knowledge has been addressed in the area of Belief Revision, a field emerging as the convergence of the efforts in Philosophy, Logic, and more recently Computer Science, where research efforts usually involve “flat” knowledge bases where there is no additional information about the formulas stored in it. Even when this may be a good fit for particular applications, in many real-world scenarios (...) different information items may be attached to formulas. For instance, when the reliability of the source of the piece of information is attached to it as a measure of some quality (e.g., strength) of the piece of information itself, or when some characteristic informs us on the desirability of the item (e.g., the potential benefit that could be obtained from it). If this type of information is available, we can use it to guide how the belief base is to be modified when new information arrives. In this work, we present a novel approach to the contraction of knowledge bases where formulas have values attached that measure some quality linked to those formulas, exploiting it to define their desirability, and uses such desirability to define which formulas need to be removed to solve conflicts. In this context, we introduce a set of properties for contraction operators by extending classic approaches. We also show how the local treatment of minimal conflicts can induce some counter-intuitive contractions, and we present a way to avoid them by considering optimal resolutions of conflicts using the additional information encoded. We show how the proposed formalization captures any contraction that is optimal under a set of features. Finally, we present a refinement based on the identification of related minimal conflicts that performs contraction in optimal ways without looking into the entire knowledge base. The approach is based on the use of the accrual of beliefs where several formulas collaboratively use their respective values to prevail in the resolution of conflicts. (shrink)

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is determined dynamically (...) during the dialectical analysis.We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly. (shrink)

In this article we explore multiple change operators, i.e., operators in which the epistemic input is a set of sentences instead of a single sentence. We propose two types of change: prioritized change, in which the input set is fully accepted, and symmetric change, where both the epistemic state and the epistemic input are equally treated. In both kinds of operators we propose a set of postulates and we present different constructions: kernel changes and partial meet changes.

We present different constructions for nonprioritized belief revision, that is, belief changes in which the input sentences are not always accepted. First, we present the concept of explanation in a deductive way. Second, we define multiple revision operators with respect to sets of sentences (representing explanations), giving representation theorems. Finally, we relate the formulated operators with argumentative systems and default reasoning frameworks.

In this paper we introduce a formalism for single-agent decision making that is based on Dynamic Argumentation Frameworks. The formalism can be used to justify a choice, which is based on the current situation the agent is involved. Taking advantage of the inference mechanism of the argumentation formalism, it is possible to consider preference relations, and conflicts among the available alternatives for that reasoning. With this formalization, given a particular set of evidence, the justified conclusions supported by warranted arguments will (...) be used by the agent’s decision rules to determine which alternatives will be selected. We also present an algorithm that implements a choice function based on our formalization. Finally, we complete our presentation by introducing formal results that relate the proposed framework with approaches of classical decision theory. (shrink)

Over the last decade, several extensions of Dung’s Abstract Argumentation Frameworks (AFs) have been introduced in the literature. Some of these extensions concern the nature of the attack relation, such as the consideration of recursive attacks, whereas others incorporate additional interactions, such as a support relation. Recently, the Attack–Support Argumentation Framework (ASAF) was proposed, which accounts for recursive attacks and supports, attacks to supports and supports to attacks, at any level, where the support relation is interpreted as necessity. Currently, to (...) determine the accepted elements of an ASAF (which may be arguments, attacks, and supports) it is required to translate such an ASAF into a Dung’s AF. In this work, we provide a formal characterization of acceptability semantics directly on the ASAF, without requiring such a translation. We prove that our characterization is sound since it satisfies different results from Dung’s argumentation theory; moreover, we formally show that the approach proposed here for addressing acceptability is equivalent to the preexisting one, in which the ASAF was translated into an AF. Also, we formalize the relationship between the ASAF and other frameworks on which it is inspired: the Argumentation Framework with Recursive Attacks (AFRA) and the Argumentation Framework with Necessities (AFN). (shrink)

This work considers the formalisation of the merging process of stratified belief bases, where beliefs are stored in different layers or strata. Their strata are ranked, following a total order, employing the value the agent using the belief base assigns to these beliefs. The agent uses an argumentation mechanism to reason from the belief base and obtain the final inferences. We present two ways of merging stratified belief bases: the first is defined by merging two strata without belief preservation, and (...) the second by merging two strata with belief preservation. For these operators, as layers merge, it is possible that some information has to be deleted from the stratum to maintain consistency. The latter merge operator will be defined as performing their actions so that information removed from the stratum is preserved after the merging by moving it to a stratum containing information perceived as having a lower value and where those beliefs may trigger a new revision, possibly starting a cascading effect. (shrink)

In abstract argumentation, each argument is regarded as atomic. There is no internal structure to an argument. Also, there is no specification of what is an argument or an attack. They are assumed to be given. This abstract perspective provides many advantages for studying the nature of argumentation, but it does not cover all our needs for understanding argumentation or for building tools for supporting or undertaking argumentation. If we want a more detailed formalization of arguments than is available with (...) abstract argumentation, we can turn to structured argumentation, which is the topic of this special issue of Argument and Computation. In structured argumentation, we assume a formal language for representing knowledge and specifying how arguments and counterarguments can be constructed from that knowledge. An argument is then said to be structured in the sense that normally, the premises and claim of the argument are made explicit, and the relationship between the premises and claim is formally defined (for instance, using logical entailment). In this introduction, we provide a brief overview of the approaches covered in this special issue on structured argumentation. (shrink)

. Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a confluence point for many alternative logical frameworks. Different formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other (...) conflicting arguments. In this context, defeasible consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators Carg and Cwar intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDSar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference operators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. (shrink)

This paper aims at comparing and relating belief revision and argumentation as approaches to model reasoning processes. Referring to some prominent literature references in both fields, we will discuss their (implicit or explicit) assumptions on the modeled processes and hence commonalities and differences in the forms of reasoning they are suitable to deal with. The intended contribution is on one hand assessing the (not fully explored yet) relationships between two lively research fields in the broad area of defeasible reasoning and (...) on the other hand pointing out open issues and potential directions for future research. (shrink)

En Faulkner llama la atención la repetición de personajes, la recurrencia a escenarios parecidos, la persistencia en memorias colectivas y la profundidad en conflictos cotidianos. Faulkner no se sale del sur, del ambiente de los vencidos, de sus imágenes más cercanas.

Pensamientos desde Berlín, pensamientos sobre Berlín; lo que el autor ve, siente, percibe y lo que capta en relación con todo su amplio bagaje de lecturas. Ver, entender, leer, del ojo a la pluma, del recuerdo a la pluma, magia o realidad de un encuentro.

Abstract. The notion of similarity has been studied in many areas of Computer Science; in a general sense, this concept is defined to provide a measure of the semantic equivalence between two pieces of knowledge, expressing how “close” their meaning can be regarded. In this work, we study similarity as a tool useful to improve the representation of arguments, the interpretation of the relations between arguments, and the semantic evaluation associated with the arguments in the argumentative process. In this direction, (...) we present a novel mechanism to determine the similarity between two arguments based on descriptors representing particular aspects associated with these arguments. This mechanism involves a comparison process influenced by the context in which the process develops, where this context provides the relevant aspects that need to be analyzed in the application domain. Then, we use this similarity measure as a quantity to compute the result of attacks and supports in the argumentation process. These valuations, applied to a Bipolar Argumentation Frameworks, allowed us to refine the argument relations, providing the tools to establish a family of new argumentation semantics that considers the similarity between arguments as a crucial part for the argumentation process. (shrink)

Defeasible argumentation has been applied successfully in several real-world domains in which it is necessary to handle incomplete and contradictory information. In recent years, there have been interesting attempts to carry out argumentation processes supported by massive repositories developing argumentative reasoning applications. One of such efforts builds arguments by retrieving information from relational databases using the DBI-DeLP framework; this article presents eDBI-DeLP, which extends the original DBI-DeLP framework by providing two novel aspects which refine the interaction between DeLP programs and (...) relational databases. First, we expand the expressiveness of dbi-delp programs by providing ways of controlling how the information in databases is recovered; this is done by introducing filters that enable an improved fine-grained control on the argumentation processes which become useful in applications, providing the semantics and the implementation of such filters. Second, we introduce an argument comparison criterion which can be adjusted at the level of literals to model particular features such as credibility and topic expertise, among others. These new tools can be particularly useful in environments such as medical diagnosis expert systems, decision support systems, or recommender systems based on argumentation, where datasets are often provided in the form of relational databases. (shrink)

We present a novel argumentation-based method for finding and analyzing communities in social media on the Web, where a community is regarded as a set of supported opinions that might be in conflict. Based on their stance, we identify argumentative coalitions to define them; then, we apply a similarity-based evaluation method over the set of arguments in the coalition to determine the level of cohesion inherent to each community, classifying them appropriately. Introducing conflict points and attacks between coalitions based on (...) argumentative (dis)similarities to model the interaction between communities leads to considering a meta-argumentation framework where the set of coalitions plays the role of the set of arguments and where the attack relation between the coalitions is assigned a particular strength which is inherited from the arguments belonging to the coalition. Various semantics are introduced to consider attacks’ strength to particularize the effect of the new perspective. Finally, we analyze a case study where all the elements of the formal construction of the formalism are exercised. (shrink)

We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having a lower value. In this manner, if the revision of one layer leads to the rejection of (...) some information to maintain consistency, instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how the status of arguments can be modified after a revision process. (shrink)

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is determined dynamically (...) during the dialectical analysis.We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly. (shrink)

Since 1969, the international chemistry community has only held conferences on the topic of the Periodic Table three times, and the 2012 conference in Cusco, Peru was the first in almost a decade. The conference was highly interdisciplinary, featuring papers on geology, physics, mathematical and theoretical chemistry, the history and philosophy of chemistry, and chemical education, from the most reputable Periodic Table scholars across the world. Eric Scerri and Guillermo Restrepo have collected fifteen of the strongest papers presented at (...) this conference, from the most notable Periodic Table scholars. The collected volume will contain pieces on chemistry, philosophy of science, applied mathematics, and science education. (shrink)

This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of biology, philosophy of technology, moral philosophy, social and political (...) philosophy, medical philosophy, and education. The contributors include scholars from 16 countries. Bunge combines ontological realism with epistemological fallibilism. He believes that science provides the best and most warranted knowledge of the natural and social world, and that such knowledge is the only sound basis for moral decision making and social and political reform. Bunge argues for the unity of knowledge. In his eyes, science and philosophy constitute a fruitful and necessary partnership. Readers will discover the wisdom of this approach and will gain insight into the utility of cross-disciplinary scholarship. This anthology will appeal to researchers, students, and teachers in philosophy of science, social science, and liberal education programmes. 1. Introduction Section I. An Academic Vocation Section II. Philosophy Section III. Physics and Philosophy of Physics Section IV. Cognitive Science and Philosophy of Mind Section V. Sociology and Social Theory Section VI. Ethics and Political Philosophy Section VII. Biology and Philosophy of Biology Section VIII. Mathematics Section IX. Education Section X. Varia Section XI. Bibliography. (shrink)

In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in intuitionistic logic, and P. Hajek proved it in the fuzzy logic BL for Grzegorczyk's variant of Q which interprets the arithmetic operations as non-total non-functional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...) weaker arithmetic theory, a version of Robinson's R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic. (shrink)

In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...) weaker arithmetic theory, a version of Robinson’s R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic. (shrink)

The point of departure for htis essay is the evaluation of democracy in Latin America, in particular, Colombian democracy following the new, 1991 Constitution. Special emphasis is placed upon the phenomena of violence, corruption and abstentionism, while a solution for these problems is sought in the strengthening of democracy in the specific form of participatory democracy, understood as a more authentic version capable of incorporating diverse cultures, classes and social movements. Recent discussions in contemporary moral and political philosophy help to (...) clarify the meaning of participatory democracy through a reconstruction of the debate between J. Habermas' discourse ethics and radical democracy, and J. Rawls' political liberalism, which has in turn been challenged by the liberal and communitarian critiques of R. Dworkin and M. Sandel, respectively. (shrink)

This paper aims to read Das Schloß by F. Kafka from a phenomenological-hermeneutic investigation project, from where to identify the “poetical mark” of the novel. Assuming this methodological perspective, it will attempt to interpret the “poetical mark” of the novel in order to mark it as the guide which leads our whole interpretation of the text, in which the distance and differences between K. and the villagers will be described. Finally, we will confront with R. Calasso’s description of the castle (...) as a place of concretion of power according to our interpretation of the scheinbare Leere from the novel’s beginning and K.’s “title” of Landvermessen. (shrink)

Counting models for a two conjunctive formula $F$, a problem known as $\sharp $2Sat, is a classic $\sharp $P complete problem. Given a 2-CF $F$ as input, its constraint graph $G$ is built. If $G$ is acyclic, then $\sharp $2Sat can be computed efficiently. In this paper, we address the case when $G$ has cycles. When $G$ is cyclic, we propose a decomposition on the constraint graph $G$ that allows the computation of $\sharp $2Sat in incremental way. Let $T$ be (...) a cactus graph of $G$ containing a maximal number of independent cycles, and let $\overline{T}=-E)$ be a subset of frond edges from $G$. The clauses in $\overline{T}$ are ordered in connected components $\{K_1, \ldots, K_r\}$. Each $, i=1,\ldots,r$ is a knot of the graph. The arrangement of the clauses of $\overline{T}$ allows the decomposition of $G$ in knots and provides a way of computing $\sharp $2Sat in an incremental way. Our procedure has a bottom-up orientation for the computation of $\sharp $2Sat. It begins with $F_0 = T$. In each iteration of the procedure, a new clause $C_i \in \overline{T}$ is considered in order to form $F_i = $ and then to compute $\sharp $2Sat$$ based on the computation of $\sharp $2Sat$$. (shrink)

This note corrects a lemma in the recent paper 1] of one of the authors by rst correcting problems with Poole's rule for speci city of arguments. It also responds to the criticism of Touretzky, et al. 9].

Reseña de la obra de Rodríguez, R. y Jaran, F. : _El proyecto de una antropología fenomenológica_, Guillermo Escolar, Madrid, 2021, 316 pp.

W illia m o f Ockha m w a s a F rancisca n fria r , a theol o gia n an d a v e r y singula r philo sophe r . H e l i v e d a t a tim e o f crisi s an d durin g th e transitio n o f philosop h y an d theol o g y . Hi s secularis m i s manifeste d i n (...) th e defens e o f a radica l separatio n bet w ee n th e religious an d secula r p ow ers . Assigne d t o th e philosophica l cu r ren t o f nominalism , h e deal t a s e v ere b l o w t o th e metap h ysica l realis m o f Aristotl e an d Thoma s Aquina s an d h e ad v ocate d the separatio n o f reaso n an d f aith , bet w ee n philosop h y an d theol o g y an d thu s h e unde r mined th e ideol o gica l foundation s o f th e churc h o f hi s time . H e w a s accuse d o f heres y because o f hi s nominalism , althoug h h e himsel f condemne d P op e Joh n XXI I a s heretica l fo r his conceptio n o f p o v e r t y , a concep t f a r rem o v e d fro m ev angelica l principle s an d especial ly fro m th e notio n o f th e F rancisca n orde r . H e defende d th e separatio n o f churc h an d stat e and h e denie d th e P ope ’ s authorit y i n secula r matters . H e flat ly asse r te d freedo m o f conscience an d Luthe r too k hi m a s a teache r. (shrink)