So-called 'Frege cases' pose a challenge for anyone who would hope to treat the contents of beliefs (and similar mental states) as Russellian propositions: It is then impossible to explain people's behavior in Frege cases without invoking non-intentional features of their mental states, and doing that seems to undermine the intentionality of psychological explanation. In the present paper, I develop this sort of objection in what seems to me to be its strongest form, but then offer a response to it. (...) I grant that psychological explanation must invoke non-intentional features of mental states, but it is of crucial importance which such features must be referenced. -/- It emerges from a careful reading of Frege's own view that we need only invoke what I call 'formal' relations between mental states. I then claim that referencing such 'formal' relations within psychological explanation does not undermine its intentionality in the way that invoking, say, neurological features would. The central worry about this view is that either (a) 'formal' relations bring narrow content in through back door or (b) 'formal' relations end up doing all the explanatory work. Various forms of each worry are discussed. The crucial point, ultimately, is that the present strategy for responding to Frege cases is not available either to the 'psycho-Fregean', who would identify the content of a belief with its truth-value, nor even to someone who would identify the content of a belief with a set of possible worlds. It requires the sort of rich semantic structure that is distinctive of Russellian propositions. There is therefore no reason to suppose that the invocation of 'formal' relations threatens to deprive content of any work to do. (shrink)

The traditional Dung networks depict arguments as atomic and study the relationships of attack between them. This can be generalised in two ways. One is to consider various forms of attack, support, feedback, etc. Another is to add content to nodes and put there not just atomic arguments but more structure, e.g. proofs in some logic or simply just formulas from a richer language. This paper offers to use temporal and modal language formulas to represent arguments in the nodes of (...) a network. The suitable semantics for such networks is Kripke semantics. We also introduce a new key concept of usability of an argument. This is the beginning of a continuing research for adding contents to the nodes of an argumentation network. This research will allow us to address notions like ?what does it exactly mean for a node to attack another? or ?what does it mean for a network to be consistent? or ?can we give proper proof rules to manipulate networks?, and more. (shrink)

This paper develops a new framework for combining propositional logics, called "juxtaposition". Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is (...) paid to the phenomenon of collapse. It is shown that there are logics with two stocks of classical or intuitionist connectives that do not collapse. Finally, the paper briefy investigates the question of which rules, when added to these logics, lead to collapse. (shrink)

We prove that everyn-modal logic betweenKnandS5nis undecidable, whenever n ≥ 3. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov–Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a reduction of the representation problem of finite relation (...) algebras. (shrink)

. The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For (...) illustration, we revisit the example of combining intuitionistic and classical propositional logics. (shrink)

Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) as well as methods for decomposing logics, showing their interesting properties (...) and applications. (shrink)

It is shown that the many-dimensional modal logic K n , determined by products of n-many Kripke frames, is not finitely axiomatisable in the n-modal language, for any $n > 2$ . On the other hand, K n is determined by a class of frames satisfying a single first-order sentence.

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...) result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in (...) the meet-combination is proved to be decidable whenever the validity problem for the components are decidable. Several examples are discussed, namely, involving modal and intuitionistic logics, as well as the meet-combination of modal logic and intuitionistic logic. (shrink)

Let us consider multimodal logics and. We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and, we construct a connected frame which characterises the fusion. The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and (...) there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point. We also describe a similar construction where we assume the existence of two classes consisting of rooted frames only. Using those classes and frames with so-called -roots, we construct a rooted frame adequate for the fusion of modal logics characterised by the classes under consideration. Both constructions can be used interchangeably. The selection of the construction depends on... (shrink)

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. (...) An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings. (shrink)

This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas (...) to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster?Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005. (shrink)

Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. (...) Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem. (shrink)

We prove that everyn-modal logic betweenKnandS5nis undecidable, whenever n ≥ 3. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov–Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a reduction of the representation problem of finite relation (...) algebras. (shrink)

We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of first-order formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language both for classical and intuitionistic fragment), we then prove that in order (...) to express well-known properties like ‘speaks-for’ or ‘hand-off’, defined in terms of says, we do not need second-order logic (unlike previous approaches) but a decidable fragment of first-order logic suffices. We propose a model-driven study of the says axiomatization by constraining the Kripke models in order to respect desirable security properties, we study how existing access control logics can be translated into FSL and we give completeness for the logic. (shrink)

Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets. Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract (...) logics. To conclude, the conceptual notion paraconsistent orbit of a logic is proposed. (shrink)

The Fregean-inspired Principle of Compositionality of Meaning for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint—that may or may not be respected—on the internal mechanisms that build and give meaning to a given formal system. Within the domain of (...) formal semantics and of the structure of logical derivations, the PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally well-behaved logical systems. (shrink)