Related papers: Tense logics based on posets
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can…
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of…
Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…
The concept of operator left residuation has been introduced by the authors in a previous paper. Modifications of so-called quantum structures, in particular orthomodular posets, like pseudo-orthomodular, pseudo-Boolean and Boolean posets…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
It is well-known that in the logic of quantum mechanics disjunctions and conjunctions can be represented by joins and meets, respectively, in an orthomodular lattice provided their entries commute. This was the reason why J. Pykacz…
The commutative and homological algebra of modules over posets is developed, as closely parallel as possible to the algebra of finitely generated modules over noetherian commutative rings, in the direction of finite presentations, primary…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
This paper presents an extension of temporal epistemic logic with operators that quantify over agent strategies. Unlike previous work on alternating temporal epistemic logic, the semantics works with systems whose states explicitly encode…
Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…
We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and…
It is known that intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth functions. We extend this generalized Kripke semantics to first-order logic, and study how…
An introduction is given to an algebraic formulation and generalisation of the consistent histories approach to quantum theory. The main technical tool in this theory is an orthoalgebra of history propositions that serves as a generalised…
The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic…