Epicurus’ Non-Propositional Theory of Truth

Scholars typically distinguish at least two different Epicurean conceptions of truth: (1) an account that pertains to the truth of perceptions or impressions and (2) an account that pertains to the truth of opinions. This paper addresses the relationship between the truth of perceptions (and by extension: preconceptions and feelings), on the one hand, and the truth of opinions, on the other. It offers an account of what these determinations of truth amount to and how they interact with each other. In doing so, the paper rejects a propositional understanding of Epicurean truth. It instead argues that the Epicurean conception of truth can be explained by relying on images and their combination.

Query Answering in Propositional Circumscription

Propositional circumscription defines a preference relation over the models of a propositional theory, so that models being subset-minimal on the interpretation of a set of objective atoms are preferred.The complexity of several computational tasks increase by one level in the polynomial hierarchy due to such a preference relation;among them there is query answering, which amounts to decide whether there is an optimal model satisfying the query.A complete algorithm for query answering is obtained by searching for a model, not necessarily an optimal one, that satisfies the query, and such that no model unsatisfying the query is more preferred.If the query or its complement are among the objective atoms, the algorithm has a simpler behavior, which is also described in the paper.Moreover, an incomplete algorithm is obtained by searching for a model satisfying both the query and an objective atom being unit-implied by the theory extended with the complement of the query.A prototypical implementation is tested on instances from the 2nd International Competition on Computational Models of Argumentation (ICCMA'17).

The property theory and de se attitudes

The property theory of de se belief denies that believing is a propositional attitude, maintaining instead that for Lingens to believe that he himself is lost is for him to self-attribute the property of being lost. For Lingens to believe that Lingens is lost is for him to self-attribute the independent property of being such that Lingens is lost. The chapter argues that this theory postulates differences where we expect uniformity, introduces unnecessary theoretical complexity, is false to a variety of linguistic and phenomenological facts, and fails to explain many psychological and linguistic facts. If “self-attribute a property” means “believing oneself to have the property,” then the theory provides no explanation of de se belief. The author sketches a propositional theory on which the objects of the attitudes are complexes of concepts (thoughts), de se attitudes involving one type of indexical concept.

Bukan Jalan Buntu, Melainkan Setapak Terjal: Sebuah Apresiasi Kritis terhadap Sumbangsih Teori Kultural-Linguistik Lindbeck bagi Penumbuhkembangan Dialog Antaragama yang Autentik

Advancing from his criticism against two principal theological theories of religion, namely (1) cognitive-propositional theory and (2) experiential-expressive theory, George A. Lindbeck proposes his cultural-linguistic theory as an alternative theory which is deemed more adequate in comprehending plurality of religions. Regrettably, for some, Lindbeck�s theory is considered rather as a closure to any interreligious dialogue, as a consequence of its superfluous emphasis on the incommensurability and untranslability amongst different religions. Therefore, within this modest article, taking into account several insights from postcolonial studies, I try to venture a critical appreciation on how Lindbeck�s cultural-linguistic theory might contribute to the endeavour of fostering constructive, authentic, and profound interreligious dialogue. I attempt to argue that Lindbeck�s cultural-linguistic theory, instead of imparting a cul-de-sac to any interreligious dialogue, actually lay bare a path for the dialogue. A path which is, whilst hard and steep, viable.

Generalized geometric theories and set-generated classes

We introduce infinitary propositional theories over a set and their models which are subsets of the set, and define a generalized geometric theory as an infinitary propositional theory of a special form. The main result is thatthe class of models of a generalized geometric theory is set-generated. Here, a class$\mathcal{X}$of subsets of a set is set-generated if there exists a subsetGof$\mathcal{X}$such that for each α ∈$\mathcal{X}$, and finitely enumerable subset τ of α there exists a subset β ∈Gsuch that τ ⊆ β ⊆ α. We show the main result in the constructive Zermelo–Fraenkel set theory (CZF) with an additional axiom, called the set generation axiom which is derivable inCZF, both from the relativized dependent choice scheme and from a regular extension axiom. We give some applications of the main result to algebra, topology and formal topology.

Strong Equivalence of Qualitative Optimization Problems

We introduce the framework of qualitative optimization problems (or, simply, optimization problems) to represent preference theories. The formalism uses separate modules to describe the space of outcomes to be compared (the generator) and the preferences on outcomes (the selector). We consider two types of optimization problems. They differ in the way the generator, which we model by a propositional theory, is interpreted: by the standard propositional logic semantics, and by the equilibrium-model (answer-set) semantics. Under the latter interpretation of generators, optimization problems directly generalize answer-set optimization programs proposed previously. We study strong equivalence of optimization problems, which guarantees their interchangeability within any larger context. We characterize several versions of strong equivalence obtained by restricting the class of optimization problems that can be used as extensions and establish the complexity of associated reasoning tasks. Understanding strong equivalence is essential for modular representation of optimization problems and rewriting techniques to simplify them without changing their inherent properties.

Reducing fuzzy answer set programming to model finding in fuzzy logics

In recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalismsallow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining thestable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where manyefficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-knowntechnique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactlycorrespond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the wayto implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners.

Guarded resolution for Answer Set Programming

We investigate a proof system based on a guarded resolution rule and show its adequacy for the stable semantics of normal logic programs. As a consequence, we show that Gelfond–Lifschitz operator can be viewed as a proof-theoretic concept. As an application, we find a propositional theory EP whose models are precisely stable models of programs. We also find a class of propositional theories 𝓒P with the following properties. Propositional models of theories in 𝓒P are precisely stable models of P, and the theories in 𝓒T are of the size linear in the size of P.