Review of Symbolic Logic 

About: Review of Symbolic Logic is an academic journal published by Association for Symbolic Logic. The journal publishes majorly in the area(s): Axiom & Modal logic. It has an ISSN identifier of 1755-0211. Over the lifetime, 552 publications have been published receiving 7118 citations.

The Logic of Justification

Abstract: We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidence-based foundation for epistemic logic.

The pure logic of ground

Abstract: I lay down a system of structural rules for various notions of ground and establish soundness and completeness. Ground is the relation of one truth holding in virtue of others. This relation is like that of consequence in that a necessary connection must hold between the relata if the relation is to obtain but it differs from consequence in so far as it required that there should also be an explanatory connection between the relata. The grounds must account for what is grounded. Thus even though P is a consequence o fPP but the claim that P is a ground fo rPP they can be assessed for consistency, assigned a semantics, compared for proof-theoretic strength, etc. There are two other, more particular, aspects of my approach. The first lies in its concep- tual basis. Most other philosophers have worked almost exclusively with a concept of strict ground, under which a truth is not capable (or, at least, not normally capable) of being a ground for itself. 2 But I believe that there is also an important concept of weak ground, under which a truth will automatically be a ground for itself. Very roughly, we may say that strict grounds must move us down in the explanatory order while weak grounds must not move us up. Thus P can weakly ground P, bu tP&P cannot weakly ground P given that P strictly grounds P & P.

A logic for 'because'

Abstract: In spite of its significance for everyday and philosophical discourse, the explanatory connective 'because' has not received much treatment in the philosophy of logic. The present paper develops a logic for 'because' based on systematic connections between 'because' and the truth- functional connectives. §1. Introduction. 1.1. The project. In the philosophy of logic, the natural language connectives 'and', 'or', 'not', and 'if . . . then' are widely discussed and so are their formal counterparts, such as the truth-functional connectives of classical logic or counterfactual and strict con- ditionals in modal systems. Considerably less attention has been paid to the explanatory connective 'because'. One simple reason may be that 'because' is quite complicated to handle. 'Because' is obviously not an extensional operator: the truth of the two clauses in a 'because'-sentence is compatible both with the truth of the sentence (JFK died because he was shot) and with its falsity (JFK died because Chernobyl exploded). But not only is 'because' nonexten- sional, it is even hyperintensional: necessarily equivalent clauses are not substitutable salva veritate in its context. This immediately follows if (i) some true 'because'-sentences have a main clause expressing a necessary truth, and (ii) not all necessary truths are explained by exactly the same things. For, assume that S expresses a necessary truth (e.g., that {2} contains a prime number), and that there is at least one true instance of S because φ (e.g., '{2} contains a prime number because it contains 2 and 2 is prime'). If 'because' was at most an intensional operator, S could be substituted salva veritate with any neces- sarily equivalent clause, that is, with any sentence expressing a necessary truth. Hence, any 'because'-clause that would explain S would equally explain any other necessary truth. (An analogous reasoning applies to necessarily true 'because'-clauses of 'because'- sentences.) But necessary truths are not the only cases that illustrate the hyperintensionality of 'because'. To wit, the majority of philosophers in the debate about truth accept the Aris- totelian insight that the following schema is valid for true instances of 'p': 1 Truth That p is true because p (but not vice versa). Given this insight, 'because' must be hyperintensional. For, the two clauses 'p' and 'that p is true' agree in truth-value with respect to every possible world. Since the clauses are furthermore cognitively equivalent (a speaker who understands them normally has to adopt the same epistemic stance towards them), the example yields the yet stronger result that

'knowable' as 'known after an announcement' ∗

Abstract: Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ♦ϕ expresses that there is a truthful announcement ψ after which ϕ is true. This logic gives a perspective on Fitch’s knowability issues: for which formulas ϕ does it hold that ϕ → ♦Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.