Standard Kripke Semantics Research Articles

Exact Truthmaker Semantics for Modal Logics

The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for “Necessarily P” is a state that bans every exact truthmaker for “Not P”, and an exact truthmaker for “Possibly P” is a state that allows an exact truthmaker for P. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of “truth at a possible world” in terms of exact truthmaking.

Recapturing Dynamic Logic of Relation Changers via Bounded Morphisms

The present contribution shows that a Hilbert-style axiomatization for dynamic logic of relation changers is complete for the standard Kripke semantics not by a well-known rewriting technique but by the idea of an auxiliary semantics studied by van Benthem and Wang et al. A key insight of our auxiliary semantics for dynamic logic of relation changers can be described as: “relation changers are bounded morphisms.” Moreover, we demonstrate that this semantic insight can be used to provide a modular cut-free labelled sequent calculus for the logic in the sense that our calculus can be regarded as a natural expansion of a labelled sequent calculus of iteration-free propositional dynamic logic.

A logic of plausible justifications

In this work, we combine features from Justification Logics and Logics of Plausibility-Based Beliefs to build a logic for Multi-Agent Systems where each agent can explicitly state his justification for believing in a given sentence. Our logic is a normal modal logic based on the standard Kripke semantics, where we provide a semantic definition for the evidence terms and define the notion of plausible evidence for an agent, based on plausibility relations in the model. As we deal with beliefs, justifications can be faulty and unreliable. In our logic, agents can disagree not only over whether a sentence is true or false, but also on whether some evidence is a valid justification for a sentence or not. After defining our logic and its semantics, we provide a strongly complete axiomatic system for it, show that it has the finite model property, analyze the complexity of its Model-Checking Problem and show that its Satisfiability Problem has the same complexity as the one from basic modal logics. Thus, this logic seems to be a good first step for the development of a dynamic logic that can model the processes of argumentation and debate in Multi-Agent Systems.

Temporal logic and its application to normative reasoning

I present a variant of with time, called (Temporal ), interpreted in standard Kripke semantics. On the syntactic level, is nothing but the extension of atemporal individual by: (i) the future tense and past tense operators, and (ii) the operator of group agency for the grand coalition (the coalition of all agents). A sound and complete axiomatisation for is given. Moreover, it is shown that supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment.

Kripke Models, Distributive Lattices, and Medvedev Degrees

We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice.

Knowledge structure approach to verification of authentication protocols

The standard Kripke semantics of epistemic logics has been applied successfully to reasoning communication protocols under the assumption that the network is not hostile. This paper introduces a natural semantics of Kripke semantics called knowledge structure and, by this kind of Kripke semantics, analyzes communication protocols over hostile networks, especially on authentication protocols. Compared with BAN-like logics, the method is automatically implementable because it operates on the actual definitions of the protocols, not on some difficult-to-establish justifications of them. What is more, the corresponding tool called SPV (Security Protocol Verifier) has been developed. Another salient point of this approach is that it is justification-oriented instead of falsification-oriented, i.e. finding bugs in protocols.

A new proof of completeness for a relative modal logic with composition and intersection

This paper is devoted to the completeness issue of RMLCI — the relative modal logic with composition and intersection— a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally definable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper “Complete axiomatization of a relative modal logic with composition and intersection”. The theorem asserts that the proof theory of RMLCI is complete for the standard Kripke semantics of RMLCI

Interpretations of intuitionist logic in non-normal modal logics

Historically, it was the interpretations of intuitionist logic in the modal logic S4 that inspired the standard Kripke semantics for intuitionist logic. The inspiration of this paper is the interpretation of intuitionist logic in the non-normal modal logic S3: an S3 model structure can be 'looked at' as an intuitionist model structure and the semantics for S3 can be 'cashed in' to obtain a non-normal semantics for intuitionist propositional logic. This non-normal semantics is then extended to intuitionist quantificational logic.

Incompleteness Results in Kripke Bundle Semantics

AbstractKripke bundle and C‐set semantics are known as semantics which generalize standard Kripke semantics. In [4] and in [1, 2] it is shown that Kripke bundle and C‐set semantics are stronger than standard Kripke semantics. Also it is true that C‐set semantics for superintuitionistic logics is stronger than Kripke bundle semantics ([6]). Modal predicate logic Q‐S4.1 is not Kripke bundle complete ([3] ‐ it is also yielded as a corollary to Theorem 6.1(a) of the present paper). This is shown by using difference of Kripke bundle semantics and C‐set semantics. In this paper, by using the same idea we show that incompleteness results in Kripke bundle semantics which are extended versions of [2].

Kripke Bundle Semantics and C-set Semantics

Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].

Subformula semantics for strong negation systems

We present a semantics for strong negation systems on the basis of the subformula property of the sequent calculus. The new models, called subformula models, are constructed as a special class of canonical Kripke models for providing the way from the cut-elimination theorem to model-theoretic results. This semantics is more intuitive than the standard Kripke semantics for strong negation systems.