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331.
This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J
Philos Logic 22(5):481–511, 1993) concerning the modelling conditions for the axioms of assertion A → ((A → B) → B) (there called c6) and permutation (A → (B → C)) → (B → (A → C)) (there called c7). We show that the modelling conditions for assertion and permutation proposed in ‘Simplified Semantics’ overgenerate. In
fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism.
The semantics provides for no models of R in which the “base point” is inconsistent. This problem is not restricted to ‘Simplified Semantics.’ The techniques
of that paper are used in Graham Priest’s textbook An Introduction to Non-Classical Logic (Priest, 2001), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the
mistake in ‘Simplified Semantics’ and propose two different corrections. 相似文献
332.
This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the Routley–Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable. 相似文献
333.
Extended Quantum Logic 总被引:1,自引:0,他引:1
The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability. 相似文献
334.
Ryszard Wójcicki 《Studia Logica》2003,73(3):323-335
The title of this paper is a theorem, which I am going to state and prove. The theorem extends from prepositional to predicate languages the result I presented in [5]. 相似文献
335.
We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties – here called CE quantifiers – one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle. 相似文献
336.
The Genesis of Possible Worlds Semantics 总被引:1,自引:0,他引:1
This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913–1921; Feys, 1924; McKinsey, 1945; Carnap, 1945–1947; McKinsey, Tarski and Jónsson, 1947–1952; von Wright, 1951; Becker, 1952; Prior, 1953–1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955–1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958–1959; Drake, 1959–1961; Kripke, 1958–1965. 相似文献
337.
Patrick Grim Randy Au Nancy Louie Robert Rosenberger William Braynen Evan Selinger Robb E. Eason 《Synthese》2008,163(2):273-297
Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’
generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’),
using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific
volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects
in terms of those games. The measure also allows for an easy comparison between different effects in terms of matrix robustness.
Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984).
The evolution of cooperation. New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling. Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice
reduction (Grim et al. 2005. Public Affairs Quarterly, 19, 95–125). 相似文献
338.
Game Semantics for the Lambek-Calculus: Capturing Directionality and the Absence of Structural Rules
In this paper, we propose a game semantics for the (associative) Lambek calculus. Compared to the implicational fragment of intuitionistic propositional calculus, the semantics deals with two features of
the logic: absence of structural rules, as well as directionality of implication. We investigate the impact of these variations
of the logic on its game semantics.
Presented by Wojciech Buszkowski 相似文献
339.
Prior’s three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued
temporal logic Q
t
and give its axiomatization and semantics. We also argue that Q
t
provides a smooth solution to the problem of future contingents.
Presented by Daniele Mundici 相似文献
340.
Joseph Almog 《Journal of Philosophical Logic》2008,37(6):549-574
The first page of Frege’s classic “Uber Sinn und Bedeutung” sets for more than a hundred years now the agenda for much of
semantics and the philosophy of mind. It presents a purported puzzle whose solution is said to call upon the “entities” of
semantics (meanings) and psychological explanation (Psychological states, beliefs, concepts). The paper separates three separate
alleged puzzles that can be read into Frege’s data. It then argues that none are genuine puzzles. In turn, much of the Frege-driven
theoretical development, motivated as an inevitable “solution”, is thrown into doubt. 相似文献