9 research outputs found
Non-transitive linear temporal logic and logical knowledge operations
© 2015 The Author, 2015. Published by Oxford University Press. All rights reserved.We study a linear temporal logic LTLNT with non-transitive time (with NEXT and UNTIL) and possible interpretations for logical knowledge operations in this approach. We assume time to be non-transitive, linear and discrete, it is a major innovative part of our article. Motivation for our approach that time might be non-transitive and comments on possible interpretations of logical knowledge operations are given. The main result of Section 5 is a solution of the decidability problem for LTLNT, we find and describe in details the decision algorithm. In Section 6 we introduce non-transitive linear temporal logic LTLNT(m) with uniform bound (m) for non-transitivity. We compare it with standard linear temporal logic LTL and the logic LTLNT - where non-transitivity has no upper bound - and show that LTLNT may be approximated by logics LTLNT(m). Concluding part of the article contains a list of open interesting problems
Intransitive temporal multi-agent’s logic, knowledge and uncertainty, plausibility
© Springer International Publishing Switzerland 2016. We study intransitive temporal logic implementing multiagent’s approach and formalizing knowledge and uncertainty. An innovative point here is usage of non-transitive linear time and multi-valued models - the ones using separate valuations Vj for agent’s knowledge of facts and summarized (agreed) valuation together with rules for computation truth values for compound formulas. The basic mathematical problems we study here are - decidability and decidability w.r.t. admissible rules. First, we study general case - the logic with non-uniform intransitivity and solve its decidability problem. Also we consider a modification of this logic - temporal logic with uniform non-transitivity and solve problem of recognizing admissibility in this logic
Multiagent Temporal Logics with Multivaluations
We study multiagent logics and use temporal relational models with multivaluations. The key distinction from the standard relational models is the introduction of a particular valuation for each agent and the computation of the global valuation using all agents’ valuations. We discuss this approach, illustrate it with examples, and demonstrate that this is not a mechanical combination of standard models, but a much more subtle and sophisticated modeling of the computation of truth values in multiagent environments. To express the properties of these models we define a logical language with temporal formulas and introduce the logics based at classes of such models. The main mathematical problem under study is the satisfiability problem. We solve it and find deciding algorithms. Also we discuss some interesting open problems and trends of possible further investigations
Inference Rules in some temporal multi-epistemic propositional logics
Multi-modal logics are among the best tools developed so far to analyse
human reasoning and agents’ interactions. Recently multi-modal
logics have found several applications in Artificial Intelligence (AI) and
Computer Science (CS) in the attempt to formalise reasoning about
the behavior of programs. Modal logics deal with sentences that are
qualified by modalities. A modality is any word that could be added to
a statement p to modify its mode of truth. Temporal logics are obtained
by joining tense operators to the classical propositional calculus, giving
rise to a language very effective to describe the flow of time. Epistemic
logics are suitable to formalize reasoning about agents possessing a
certain knowledge. Combinations of temporal and epistemic logics are
particularly effective in describing the interaction of agents through the
flow of time. Although not yet fully investigated, this approach has
found many fruitful applications. These are concerned with the development
of systems modelling reasoning about knowledge and space,
reasoning under uncertainty, multi-agent reasoning et c.
Despite their power, multi modal languages cannot handle a changing
environment. But this is exactly what is required in the case of human
reasoning, computation and multi-agent environment. For this purpose,
inference rules are a core instrument. So far, the research in this
field has investigated many modal and superintuitionistic logics. However,
for the case of multi-modal logics, not much is known concerning
admissible inference rules.
In our research we extend the investigation to some multi-modal propositional logics which combine tense and knowledge modalities. As far
as we are concerned, these systems have never been investigated before.
In particular we start by defining our systems semantically; further we
prove such systems to enjoy the effective finite model property and to
be decidable with respect to their admissible inference rules. We turn
then our attention to the syntactical side and we provide sound and
complete axiomatic systems. We conclude our dissertation by introducing
the reader to the piece of research we are currently working on.
Our original results can be found in [9, 4, 11] (see Appendix A). They
have also been presented by the author at some international conferences
and schools (see [8, 10, 5, 7, 6] and refer to Appendix B for more
details).
Our project concerns philosophy, mathematics, AI and CS. Modern
applications of logic in CS and AI often require languages able to represent
knowledge about dynamic systems. Multi-modal logics serve
these applications in a very efficient way, and we would absorb and
develop some of these techniques to represent logical consequences in
artificial intelligence and computation
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book
Decidability w.r.t. logical consecutions of linear temporal logic extended by since and previous
This paper aims to prove that the linear temporal logic LTLu,sn, n-1(N) , which is an extension of the standard linear temporal logic LTL by operations Since and Previous (LTL itself, as standard, uses only Until and Next) and is based on the frame of all natural numbers N, as generating Kripke/Hintikka structure, is decidable w.r.t. admissible consecutions (inference rules). We find an algorithm recognizing consecutions admissible in LTLu,sn, n-1(N) . As a consequence this algorithm solves satisfiability problem and shows that LTLu,sn, n-1(N) itself is decidable, despite LTLu,sn, n-1(N) does not have the finite model property
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established