Mechanistic interpretability is the program of explaining what AI systems are doing in terms of their internal mechanisms. I analyze some aspects of the program, along with setting out some concrete challenges and assessing progress to date. I argue for the importance of propositional interpretability, which involves interpreting a system’s mechanisms and behav- ior in terms of propositional attitudes: attitudes (such as belief, desire, or subjective probabil- ity) to propositions (e.g. the proposition that it is hot outside). (...) class='Hi'>Propositional attitudes are the central way that we interpret and explain human beings and they are likely to be central in AI too. A central challenge is what I call thought logging: creating systems that log all of the rel- evant propositional attitudes in an AI system over time. I examine currently popular methods of interpretability (such as probing, sparse auto-encoders, and chain of thought methods) as well as philosophical methods of interpretation (including those grounded in psychoseman- tics) to assess their strengths and weaknesses as methods of propositional interpretability. (shrink)

Peter Hanks defends a new theory about the nature of propositional content, according to which the basic bearers of representational properties are particular mental or spoken actions. He explains the unity of propositions and provides new solutions to a long list of puzzles and problems in philosophy of language.

Skyrms, building on the work of Dretske, has recently developed a novel information-theoretic account of propositional content in simple signalling systems. Information-theoretic accounts of content traditionally struggle to accommodate the possibility of misrepresentation, and I show that Skyrms’s account is no exception. I proceed to argue, however, that a modified version of Skyrms’s account can overcome this problem. On my proposed account, the propositional content of a signal is determined not by the information that it actually carries, but (...) by the information that it would carry at the nearest separating equilibrium of the underlying evolutionary dynamics. I show that this amended account yields reasonable ascriptions of false propositional content in a well-known formal model of the evolution of communication (the ‘Philip Sidney’ game), and close with a discussion of the serious but perhaps not insuperable difficulties we face in applying the account to examples of signalling in the real world. (shrink)

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method B p , which specifies an initial belief state B p (T) that is revised to the new propositional belief state B(E) upon receipt of information E. An acceptance rule tracks Bayesian conditioning when B p (E) = B (...) p|E (T), for every E such that p(E) > 0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The "Lockean" rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1-2):221-262, 1975; Alchourrón et al., J Symb Log 50:510-530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987). (shrink)

The tableau-like system KE is generalized to intuitionistic propositional logic by means of labeled signed formulas and constraints between labels, mimicking the relational semantics. To improve on proof-search and exploiting the meaning of negation, we further endow the system with free-variables. The resulting system enjoys the subformula property and terminates, either with a proof or a finite countermodel, without any extra mechanism. Proof and countermodel search is guided by generalizations of traditional reasoning patterns.

Philosophical writing on gratitude displays a pronounced preference for targeted gratitude (A’s being grateful to B for x) over propositional gratitude (A’s being grateful that p), treating the latter as a poor, less interesting cousin of the former, when it treats it at all. This paper challenges and attempts to rectify the relegation of propositional gratitude to second-class status. It argues that propositional gratitude is not only not reducible to targeted gratitude but indeed is more basic than (...) it and that propositional gratitude is morally important because of its conceptual connections to the virtue of humility. (shrink)

Peter Hanks and Scott Soames have recently developed similar views of propositional attitudes on which they consist at least partly of being disposed to perform mental acts. Both think that to believe a proposition is at least partly to be disposed to perform the primitive propositional act: one the performance of which is part of the performance of any other propositional act. However, they differ over whether the primitive act is the forceless entertaining or the forceful judging. (...) In this paper I argue that Soames’s “forceless” approach has an advantage over Hanks’s “forceful” approach which faces a serious problem. (shrink)

A number of philosophers and logicians have argued for the conclusion that maps are logically tractable modes of representation by analyzing them in propositional terms. But in doing so, they have often left what they mean by "propositional" undefined or unjustified. I argue that propositions are characterized by a structure that is digital, universal, asymmetrical, and recursive. There is little positive evidence that maps exhibit these features. Instead, we can better explain their functional structure by taking seriously the (...) observation that maps arrange their constituent elements in a non-hierarchical, holistic structure. This is compatible with the more basic claim advanced by defenders of a propositional analysis: that (many) maps do have formal semantics and logic. (shrink)

Prevailing approaches to interpreting large language models (LLMs) risk addressing the field’s central questions at the wrong level of analysis. As LLMs develop, researchers have turned to “under-thehood” methods to investigate whether LLMs possess states analogous to beliefs, desires, or intentions. These methods typically map internal representations, feature directions, or neural circuits onto folk-psychological categories. We argue that these methods are too fragile to reap the results we need. Instead, interpretability ought to be reoriented toward and grounded in what we (...) call “ecologically sensitive behavioral analyses” which integrates mechanistic tools with severe testing of behavioral signatures across ecological contexts, aligning interpretability efforts with emerging evaluation sciences for AI. We outline a multi-disciplinary trajectory for developing interpretability methods that are both philosophically coherent and practically relevant for the deployment of increasingly capable LLMs. (shrink)

A prospective introduction -- The received view -- Troubles with the received view -- Are propositional attitudes relations? -- Foundations of a measurement-theoretic account of the attitudes -- The basic measurement-theoretic account -- Elaboration and explication of the proposed measurement-theoretic account.

Skyrms, building on the work of Dretske, has recently developed a novel information-theoretic account of propositional content in simple signalling systems. Information-theoretic accounts of content traditionally struggle to accommodate the possibility of misrepresentation, and I show that Skyrms’s account is no exception. I proceed to argue, however, that a modified version of Skyrms’s account can overcome this problem. On my proposed account, the propositional content of a signal is determined not by the information that it actually carries, but (...) by the information that it would carry at the nearest separating equilibrium of the underlying evolutionary dynamics. I show that this amended account yields reasonable ascriptions of false propositional content in a well-known formal model of the evolution of communication (the ‘Philip Sidney’ game), and close with a discussion of the serious but perhaps not insuperable difficulties we face in applying the account to examples of signalling in the real world. (shrink)

Beliefs have what I will call ‘propositional content’. A belief is always a belief that so-and-so: a belief that grass is green, or a belief that snow is white, or whatever. Other things have propositional content too, such as sentences, judgments and assertions. The Standard View amongst philosophers is that what it is to have a propositional content is to stand in an appropriate relation to a proposition. Moreover, on this view, propositions are objects, i.e. the kind (...) of thing you can refer to with singular terms. For example, on the Standard View, we should parse the sentence ‘Simon believes that Sharon is funny’ as: [Simon] believes [that Sharon is funny]; ‘Simon’ is a term referring to a thinking subject, ‘that Sharon is funny’ is a term referring to a proposition, and ‘x believes y’ is a dyadic predicate expressing the believing relation. In this paper, I argue against the Standard View. This is how I think we should parse ‘Simon believes that Sharon is funny’: [Simon] believes that [Sharon is funny]; here we have a singular term, ‘Simon’, a sentence ‘Sharon is funny’, and a ‘prenective’ joining them together, ‘x believes that p’. On this Prenective View, we do not get at the propositional content of someone’s belief by referring to a reified proposition with a singular term; we simply use the sentence ‘Sharon is funny’ to express that content for ourselves. I argue for the Prenective View in large part by showing that an initially attractive version of the Standard View is actually vulnerable to the same objection that Wittgenstein used against Russell’s multiple-relation theory of judgment. (shrink)

One important distinction in the debate over the nature of epistemic justification is the one between propositional and doxastic justification. Roughly, while doxastic justification is a property of beliefs, propositional justification is a property of propositions. On a rather common view, which accounts for doxastic justification in terms of propositional justification plus the so-called ‘basing relation’, propositional justification is seen as the prior notion, and doxastic justification is explained in terms of it. According to the opposing (...) view, the direction of explanation needs to be reversed, and doxastic justification should be seen as primary. I distinguish between two notions of priority, and I argue that they give different verdicts with respect to the issue of which notion of justification comes first. The lesson may be taken to be that propositional and doxastic justification are in a relation of intertwinement. (shrink)

It is almost universally accepted that the Frege–Geach Point is necessary for explaining the inferential relations and compositional structure of truth-functionally complex propositions. I argue that this claim rests on a disputable view of propositional structure, which models truth-functionally complex propositions on atomic propositions. I propose an alternative view of propositional structure, based on a certain notion of simulation, which accounts for the relevant phenomena without accepting the Frege–Geach Point. The main contention is that truth-functionally complex propositions do (...) not include as their parts truth-evaluable propositions, but their simulations, which are neither forceful nor truth-evaluable. The view makes room for the idea that there is no such thing as the forceless expression of propositional contents and is attractive because it provides the resources for avoiding a fundamental problem generated by the Frege–Geach Point concerning the relation between forceless and forceful expressions of propositional contents. I further argue that the acceptance of the Frege–Geach Point mars Peter Hanks’ and François Recanati’s recent attempts to resist the widespread idea that assertoric force is extrinsic to the expression of propositional contents. Rejecting this idea, I maintain, requires a deeper break with the tradition than Hanks and Recanati have allowed for. (shrink)

If a subject has a true belief, and she has good evidence for it, and there’s no evidence against it, why should it matter if she doesn’t believe on the basis of the good available evidence? After all, properly based beliefs are no likelier to be true than their corresponding improperly based beliefs, as long as the subject possesses the same good evidence in both cases. And yet it clearly does matter. The aim of this paper is to explain why, (...) and in the process delineate a species of epistemic luck that has hitherto gone unnoticed—what we call propositional epistemic luck—but which we claim is crucial to accounting for the importance of proper basing. As we will see, in order to understand why this type of epistemic luck is malignant, we also need to reflect on the relationship between epistemic luck and epistemic risk. (shrink)

Most contemporary philosophical discussions of intentionality start and end with a treatment of the propositional attitudes. In fact, many theorists hold that all attitudes are propositional attitudes. Our folk-psychological ascriptions suggest, however, that there are non-propositional attitudes: I like Sally, my brother fears snakes, everyone loves my grandmother, and Rush Limbaugh hates Obama. I argue that things are as they appear: there are non-propositional attitudes. More specifically, I argue that there are attitudes that relate individuals to (...) non-propositional objects and do so not in virtue of relating them to propositions. I reach this conclusion by not only showing that attempted analyses of apparently non-propositional attitudes in terms of the propositional fail, but that some non-propositional attitudes don’t even supervene on propositional attitudes. If this is correct, then the common discussions of intentionality that address only propositional attitudes are incomplete and those who hold that all intentional states are propositional are mistaken. (shrink)

The philosophical case for extended cognition is often made with reference to ‘extended-memory cases’ (e.g. Clark & Chalmers 1998); though, unfortunately, proponents of the hypothesis of extended cognition (HEC) as well as their adversaries have failed to appreciate the kinds of epistemological problems extended-memory cases pose for mainstream thinking in the epistemology of memory. It is time to give these problems a closer look. Our plan is as follows: in §1, we argue that an epistemological theory remains compatible with HEC (...) only if its epistemic assessments do not violate what we call ‘the epistemic parity principle’. In §2, we show how the constraint of respecting the epistemic parity principle stands in what appears to be a prima facie intractable tension with mainstream thinking about cases of propositional memory. We then outline and evaluate in §3 several lines of response. (shrink)

Gupta develops a highly original and comprehensive account of the epistemic role of perceptual experience in his recent book. Among other things, Gupta holds that although we can attribute propositional content to experience, this alleged content has no crucial role to play in perceptual epistemology. He also adds that the view that experience justifies belief in its propositional content results in the view that experience grounds direct knowledge only of objects that are both metaphysically and logically distinct from (...) ordinary external objects, a view that he calls Cartesianism. Here, I pose two challenges to Gupta’s rejection of the epistemic significance of content and his contention that the propositional given view results in a form of Cartesianism. (shrink)

According to relationism, for Alice to believe that some rabbits can speak is for Alice to stand in a relation to a further entity, some rabbits can speak. But what could this further entity possibly be? Higher-order metaphysics seems to offer a simple, natural answer. On this view (roughly put), expressions in different syntactic categories (for instance: names, predicates, sentences) in general denote entities in correspondingly different ontological categories. Alice's belief can thus be understood to relate her to a sui (...) generis entity denoted by "some rabbits can speak", belonging to a different ontological category than Alice herself. This straightforward account of the attitudes has historically been deemed so attractive that it was seen as providing an important motivation for higher-order metaphysics itself (Prior [1971]). But I argue that it is not as straightforward as it might seem, and in fact that propositional attitudes present a foundational challenge for higher-order metaphysics. (shrink)

Propositional attitudes are often classified as non-phenomenal mental states. I argue that there is no good reason for doing so. The unwillingness to view propositional attitudes as being essentially phenomenal stems from a biased notion of phenomenality, from not paying sufficient attention to the idioms in which propositional attitudes are usually reported, from overlooking the considerable degree to which different intentional modes can be said to be phenomenologically continuous, and from not considering the possibility that propositional (...) attitudes may be transparent, just like sensations and emotions are commonly held to be: there may be no appropriate way of describing their phenomenal character apart from describing the properties and objects they represent. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation (...) and prove two new theorems. Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggrega tion rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In (...) particular, we show that the propositional connectives that are definable in terms of Frege’s horizontal, negation, and conditional are exactly the connectives that fuse with the horizontal, and we show that the logical operators that are definable in terms of the horizontal, negation, the conditional, and identity are exactly the operators that are invariant with respect to permutations on the domain that leave the truth-values fixed. We conclude with some general observations regarding how Frege understood his logic, and how this understanding differs from modern views. (shrink)

An important question in epistemology concerns how the two species of justification, propositional and doxastic justification, are related to one another. According to the received view, basing one’s belief p on the grounds that provide propositional justification to believe p is sufficient for the belief to be doxastically justified. In a recent paper, however, John Turri has suggested that we should reverse the direction of explanation. In this paper, I propose to see the debate in a new light (...) by suggesting that the best way to understand the relationship between these species of justification is by viewing propositional justification as an dispositional property that a subject can have with doxastic justification as its manifestation. I show how the debate in metaphysics over the question of how disposition statements should be analyzed runs parallel to the epistemological debate, and bring some of the results in the dispositions debate to bear on the epistemological question. I end by offering some tentative remarks regarding the order of priority of these two species of justification. (shrink)

The questions of whether episodic memory is a propositional attitude, and of whether it has propositional content, are central to discussions about how memory represents the world, what mental states should count as memories, and what kind of beings are capable of remembering. Despite its importance to such topics, these questions have not been addressed explicitly in the recent literature in philosophy of memory. In one of the very few pieces dealing with the topic, Fernández (2006) provides a (...) positive answer to the initial questions by arguing that the propositional attitude view of memory, as I will call it, provides a simple account of how memory possesses truth-conditions. A similar suggestion is made by Byrne (2010) when he proposes that perception and episodic memory have the same kind of content, differing only in degree. Against the propositional attitude view, I will argue that episodic memory does not have propositional content, and therefore, that it is not a propositional attitude. My project here is, therefore, mainly critical. I will show that, if empirical work is to inform our philosophical theories of memory in any way, we have good reasons to deny, or at least to be skeptical, of the prospects of the propositional attitude view of episodic memory. (shrink)

The concept of a proposition is important in several areas of philosophy and central to the philosophy of language. This collection of readings investigates many different philosophical issues concerning the nature of propositions and the ways they have been regarded through the years. Reflecting both the history of the topic and the range of contemporary views, the book includes articles from Bertrand Russell, Gottlob Frege, the Russell-Frege Correspondence, Alonzo Church, David Kaplan, John Perry, Saul Kripke, Hilary Putnam, Mark Richard, Scott (...) Soames, and Nathan Salmon. (shrink)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of (...) generalizations, not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

An ascent routine (AR) allows a speaker to self-ascribe a given propositional attitude (PA) by redeploying the process that generates a corresponding lower level utterance. Thus, we may report on our beliefs about the weather by reporting (under certain constraints) on the weather. The chief criticism of my AR account of self-ascription, by Alvin Goldman and others, is that it covers few if any PA’s other than belief and offers no account of how we can attain reliability in identifying (...) our attitude as belief, desire, hope, etc., without presupposing some sort of recognition process. The criticism can be answered, but only by giving up a tacit—and wholly unnecessary—assumption that has influenced discussions of ascent routines. Abandoning the assumption allows a different account of ARs that avoids the criticism and even provides an algorithm for finding a corresponding lower level utterance for any PA. The account I give is supported by research on children’s first uses of a propositional attitude vocabulary. (shrink)

Those arguing for the existence of non-propositional content appeal to emotions for support, although there has been little engagement in those debates with developments in contemporary theory of emotion, specifically in connection with the kind of mental states that emotional experiences are. Relatedly, within emotion theory, one finds claims that emotional experiences per se have non-propositional content without detailed argument. This paper argues that the content of emotional experience is propositional in a weak sense, associated with aspectual (...) experience and correctness conditions. Furthermore, it provides an interpretation of purely-objectual emotional experiences which satisfies this weak view of propositional content. (shrink)

This chapter explores solutions to a somewhat underappreciated family of puzzles concerning propositional attitudes generated by intensionalism—the view that necessarily equivalent propositions are identical. After presenting the puzzles informally, the chapter introduces the apparatus of higher-order logic, which allows one to quantify into the position of any type of expression, and makes possible a formally rigorous statement of the puzzles. Many philosophers will think that it’s quite obvious how one should respond to the puzzles—namely by treating them as refutations (...) of intensionalism. But this response is arguably too quick. The chapter explores strategies for responding to the puzzles within the framework of intensionalism, laying out a taxonomy of such strategies. Certain of these strategies treat English attitude sentences as opaque and others don’t. However all of them use a transparent (i.e. non-opaque) language as the vehicle for theorizing. The focus here will be on the logical ramifications of the various strategies. (shrink)

The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was put into (...) a canonical form, called its finest splitting. In the first part of this paper, we recall the ideas of Rodrigues and Parikh, and show that they yield equivalent definitions of what may be called canonical cell/path relevance. The second part presents the main new result of the paper: while the relation of canonical relevance is syntax-independent in the usual sense of the term, it nevertheless remains language-dependent in a deeper sense, as is shown with an example. The final part of the paper turns to questions of application, where we present a new concept of parameter-sensitive relevance that relaxes the Rodrigues/Parikh definition, allowing it to take into account extra-logical sources as well as purely logical ones. (shrink)

A novel normal form for propositional theories underlies the logic pdl, which captures some essential features of natural discourse, independent from any particular subject matter and related only to its referential structure. In particular, pdlallows to distinguish vicious circularity from the innocent one, and to reason in the presence of inconsistency using a minimal number of extraneous assumptions, beyond the classical ones. Several, formally equivalent decision problems are identified as potential applications: non-paradoxical character of discourses, admissibility of arguments in (...) argumentation networks, propositional satisfiability, and the existence of kernels of directed graphs. Directed graphs provide the basis for the semantics of pdl and the paper concludes by an overview of relevant graph-theoretical results and their applications in diagnosing paradoxical character of natural discourses. (shrink)

This essay explores questions first posed by Ernst Tugendhat: Can Edmund Husserl’s conception of truth help philosophers connect the concept of propositional truth with a more comprehensive and life-oriented idea of truth? Can it do so without short-circuiting either side? If so, to what extent? I focus on the conception of truth in Husserl’s path breaking Logical Investigations, originally published in 1900-01. First, I review critical interpretations of Husserl by three influential post-Heideggerian philosophers: Emmanuel Levinas, Theodor Adorno, and Jacques (...) Derrida. Next, I examine selected passages in the Logical Investigations. Finally, I initiate a critical retrieval of early Husserl’s conception of truth, one that not only evaluates his contribution in light of influential assessments by Levinas, Adorno, and Derrida but also proposes revisions to it. (shrink)

Trenton Merricks presents an original argument for the existence of propositions, and defends an account of their nature. He draws a variety of controversial conclusions, for instance about supervaluationism, the nature of possible worlds, truths about non-existent entities, and whether and how logical consequence depends on modal facts.

Propositions play a central role in contemporary semantics. On the Russellian account, propositions are structured entities containing particulars, properties and relations. This contrasts sharply with the sets-of-possible-worlds view of propositions. I’ll discuss how to extend the sets-of-worlds view to accommodate fine-grained hyperintensional contents. When this is done in a satisfactory way, I’ll argue, it makes heavy use of entities very much like Russellian tuples. The two notions of proposition become inter-definable and inter-substitutable: they are not genuinely distinct accounts of how (...) propositions represent what they represent. Semantic theorists may move freely between the two conceptions of what propositions are. Nevertheless, the two approaches give different accounts of the metaphysical nature of propositions. I argue that the sets-of-worlds view provides an adequate account of the nature of propositions, whereas the Russellian view cannot. (shrink)

Literature in epistemology tends to suppose that there are three main types of understanding – propositional, atomistic, and objectual. By showing that all apparent instances of propositional understanding can be more plausibly explained as featuring one of several other epistemic states, this paper argues that talk of propositional understanding is unhelpful and misleading. The upshot is that epistemologists can do without the notion of propositional understanding.

In this work, an intuitionistic propositional logic with a Galois connection is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to both of these semantics. We show that IntGC has the finite model property and is decidable, but Glivenko's Theorem does not (...) hold. Duality between algebraic and Kripke semantics is presented, and a representation theorem for Heyting algebras with Galois connections is proved. In addition, an application to rough L-valued sets is presented. (shrink)

Propositions are often aligned with truth-conditions. The view is mistaken, since propositions discriminate where truth conditions do not. Propositions are hyperintensional: they are sensitive to necessarily equivalent differences. I investigate an alternative view on which propositions are truthmaker conditions, understood as sets of possible truthmakers. This requires making metaphysical sense of merely possible states of affairs. The theory that emerges illuminates the semantic phenomena of samesaying, subject matter, and aboutness.

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L_D and L_I, based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. (...) We argue that L_D and L_I naturally resolve a range of interpretational problems that arise in D and I.We also obtain sound and complete axiomatizations for L_D and L_I . (shrink)

According to relevance theory, irony comprehension invariably entails the identification of some opinion or thought and the identification of the speaker’s dissociative attitude. In this paper, it is argued that it is also essential for hearers to identify not only that propositional attitude, but also the affective attitude that the speaker holds towards the source of this echo so that an optimallyrelevant interpretive outcomeis achieved. This notion comprises feelings and emotions of a non-propositional quality which affect the (...) class='Hi'>propositional effects obtained in ironical communication. The paper further argues for the need to incorporate non-propositional effects into the traditional propositional object of pragmatic research. (shrink)

I argue first that attention is a (maybe the) paradigmatic case of an object-directed, non-propositional intentional mental episode. In addition attention cannot be reduced to any other (propositional or non-propositional) mental episodes. Yet, second, attention is not a non-propositional mental attitude. It might appear puzzling how one could hold both of these claims. I show how to combine them, and how that combination shows how propositionality and non-propositionality can co-exist in a mental life. The crucial move (...) is one away from an atomistic, building block picture to a more holistic, structural picture. (shrink)

Partial consistency statements can be expressed as polynomial-size propositional formulas. Frege proof systems have polynomial-size partial self-consistency proofs. Frege proof systems have polynomial-size proofs of partial consistency of extended Frege proof systems if and only if Frege proof systems polynomially simulate extended Frege proof systems. We give a new proof of Reckhow's theorem that any two Frege proof systems p-simulate each other. The proofs depend on polynomial size propositional formulas defining the truth of propositional formulas. These are (...) already known to exist since the Boolean formula value problem is in alternating logarithmic time; this paper presents a proof of this fact based on a construction which is somewhat simpler than the prior proofs of Buss and of Buss-Cook- Gupta-Ramachandran. (shrink)

In the previous paper with a similar title :311–344, 2018), we presented a family of propositional epistemic logics whose languages are extended by two ingredients: by quantification over modal operators or over agents of knowledge and by predicate symbols that take modal operators as arguments. We denoted this family by \}\). The family \}\) is defined on the basis of a decidable higher-order generalization of the loosely guarded fragment of first-order logic. And since HO-LGF is decidable, we obtain the (...) decidability of logics of \}\). In this paper we construct an alternative family of decidable propositional epistemic logics whose languages include ingredients and. Denote this family by \}\). Now we will use another decidable fragment of first-order logic: the two variable fragment of first-order logic with two equivalence relations +2E) [the decidability of FO\+2E was proved in Kieroński and Otto :729–765, 2012)]. The families \}\) and \}\) differ in the expressive power. In particular, we exhibit classes of epistemic sentences considered in works on first-order modal logic demonstrating this difference. (shrink)