scholarly journals The Ceteris Paribus Structure of Logics of Game Forms (Extended Abstract)

2017 ◽  
Author(s):  
Davide Grossi ◽  
Emiliano Lorini ◽  
François Schwarzentruber
Keyword(s):  
Normal Form ◽  
Dynamic Logic ◽  
Satisfiability Problem ◽  
Ceteris Paribus ◽  
Coalition Logic ◽  
Polynomial Reduction ◽  
Complexity Result ◽  
Game Forms

We present a simple Ceteris Paribus Logic (CP) and study its relationship with existing logics that deal with the representation of choice and power in games in normal form including atemporal STIT, Coalition Logic of Propositional Control (CL-PC) and Dynamic Logic of Propositional Assignments (DL-PA). Thanks to the polynomial reduction of the satisfiability problem for atemporal STIT in the satisfiability problem for CP, we obtain a complexity result for the latter problem.

scholarly journals The Ceteris Paribus Structure of Logics of Game Forms

2015 ◽  
Vol 53 ◽  
pp. 91-126 ◽  
Author(s):  
Davide Grossi ◽  
Emiliano Lorini ◽  
Francois Schwarzentruber
Keyword(s):  
Modal Logic ◽  
Dynamic Logic ◽  
Strategic Interaction ◽  
Equivalence Classes ◽  
Finite Sets ◽  
Ceteris Paribus ◽  
Coalition Logic ◽  
Game Forms

The article introduces a ceteris paribus modal logic, called CP, interpreted on the equivalence classes induced by finite sets of propositional atoms. This logic is studied and then used to embed three logics of strategic interaction, namely atemporal STIT, the coalition logic of propositional control (CL−PC) and the starless fragment of the dynamic logic of propositional assignments (DL−PA). The embeddings highlight a common ceteris paribus structure underpinning the key operators of all these apparently very different logics and show, we argue, remarkable similarities behind some of the most influential formalisms for reasoning about strategic interaction

scholarly journals On the Conditional Logic of Simulation Models

2018 ◽  
Author(s):  
Duligur Ibeling ◽  
Thomas Icard
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Simulation Models ◽  
Conditional Reasoning ◽  
Satisfiability Problem ◽  
Simulation Program ◽  
Conditional Logic ◽  
Simulation Approach ◽  
Np Completeness ◽  
Complexity Result

We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a series of axiomatizations, allowing comparison between this framework and existing frameworks (normality-ordering models, causal structural equation models), and a complexity result establishing NP-completeness of the satisfiability problem. Perhaps surprisingly, some of the basic logical principles common to all existing approaches are invalidated in our causal simulation approach. We suggest that this additional flexibility is important in modeling some intuitive examples.

Algorithm for Decision Procedure in Temporal Logic Treating Uncertainty, Plausibility, Knowledge and Interacting Agents

2012 ◽  
pp. 32-46
Author(s):  
V. Rybakov
Keyword(s):  
Normal Form ◽  
Temporal Logic ◽  
Decision Procedure ◽  
Linear Temporal Logic ◽  
Satisfiability Problem ◽  
Global Knowledge ◽  
Interacting Agents ◽  
Logical Operations ◽  
Multi Agent ◽  
Bounded Size

Our paper studies a logic UIALTL, which is a combination of the linear temporal logic LTL, a multi-agent logic with operation for passing knowledge via agents’ interaction, and a suggested logic based on operation of logical uncertainty. The logical operations of UIALTL also include (together with operations from LTL) operations of strong and weak until, agents’ knowledge operations, operation of knowledge via interaction, operation of logical uncertainty, the operations for environmental and global knowledge. UIALTL is defined as a set of all formulas valid at all Kripke-Hintikka like models NC. Any frame NC represents possible unbounded (in time) computation with multi-processors (parallel computational units) and agents’ channels for connections between computational units. The main aim of our paper is to determine possible ways for computation logical laws of UIALTL. Principal problems we are dealing with are decidability and the satisfiability problems for UIALTL. We find an algorithm which recognizes theorems of UIALTL (so we show that UIALTL is decidable) and solves satisfiability problem for UIALTL. As an instrument we use reduction of formulas to rules in the reduced normal form and a technique to contract models NC to special non-UIALTL-models, and, then, verification of validity these rules in models of bounded size. The paper uses standard results from non-classical logics based on Kripke-Hintikka models.

MULTILINEAR EQUATIONS IN AMALGAMS OF FINITE INVERSE SEMIGROUPS

2011 ◽  
Vol 21 (01n02) ◽  
pp. 35-59 ◽  
Author(s):  
A. CHERUBINI ◽  
C. NUCCIO ◽  
E. RODARO
Keyword(s):  
Normal Form ◽  
Inverse Semigroups ◽  
Satisfiability Problem ◽  
Finite Set ◽  
Context Free ◽  
Schützenberger Automaton ◽  
Amalgamated Product

Let S = S1 *U S2 = Inv〈X; R〉 be the free amalgamated product of the finite inverse semigroups S1, S2 and let Ξ be a finite set of unknowns. We consider the satisfiability problem for multilinear equations over S, i.e. equations wL ≡ wR with wL, wR ∈ (X ∪ X-1 ∪ Ξ ∪ Ξ-1)+ such that each x ∈ Ξ labels at most one edge in the Schützenberger automaton of either wL or wR relative to the presentation 〈X ∪ Ξ|R〉. We prove that the satisfiability problem for such equations is decidable using a normal form of the words wL, wR and the fact that the language recognized by the Schützenberger automaton of any word in (X ∪ X-1)+) relative to the presentation 〈X|R〉 is context-free.

scholarly journals A General Multi-agent Epistemic Planner Based on Higher-order Belief Change

2017 ◽  
Author(s):  
Xiao Huang ◽  
Biqing Fang ◽  
Hai Wan ◽  
Yongmei Liu
Keyword(s):  
Normal Form ◽  
Belief Change ◽  
Common Knowledge ◽  
Dynamic Logic ◽  
Higher Order ◽  
Experimental Results ◽  
General Representation ◽  
Multi Agent ◽  
Representation Language ◽  
Contingent Planning

In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper, we propose a general representation language for multi-agent epistemic planning where the initial KB and the goal, the preconditions and effects of actions can be arbitrary multi-agent epistemic formulas, and the solution is an action tree branching on sensing results.To support efficient reasoning in the multi-agent KD45 logic, we make use of a normal form called alternative cover disjunctive formula (ACDF). We propose basic revision and update algorithms for ACDF formulas. We also handle static propositional common knowledge, which we call constraints. Based on our reasoning, revision and update algorithms, adapting the PrAO algorithm for contingent planning from the literature, we implemented a multi-agent epistemic planner called MAEP. Our experimental results show the viability of our approach.

Conservative reduction classes of Krom formulas

1982 ◽  
Vol 47 (1) ◽  
pp. 110-130 ◽  
Author(s):  
Stål O. Aanderaa ◽  
Egon Börger ◽  
Harry R. Lewis
Keyword(s):  
Normal Form ◽  
Decision Problem ◽  
Conjunctive Normal Form ◽  
Satisfiability Problem ◽  
Quantification Theory ◽  
Finite Models ◽  
Reduction Class

AbstractA Krom formula of pure quantification theory is a formula in conjunctive normal form such that each conjunct is a disjunction of at most two atomic formulas or negations of atomic formulas. Every class of Krom formulas that is determined by the form of their quantifier prefixes and which is known to have an unsolvable decision problem for satisfiability is here shown to be a conservative reduction class. Therefore both the general satisfiability problem, and the problem of satisfiability in finite models, can be effectively reduced from arbitrary formulas to Krom formulas of these several prefix types.

scholarly journals Dynamic logic of parallel propositional assignments and its applications to planning

2019 ◽  
Author(s):  
Andreas Herzig ◽  
Frédéric Maris ◽  
Julien Vianey
Keyword(s):  
Model Checking ◽  
Dynamic Logic ◽  
Satisfiability Problem ◽  
Parallel Composition ◽  
Conditional Effects

We introduce a dynamic logic with parallel composition and two kinds of nondeterministic composition, exclusive and inclusive. We show PSPACE completeness of both the model checking and the satisfiability problem and apply our logic to sequential and parallel classical planning where actions have conditional effects.

scholarly journals The Incremental Satisfiability Problem for a Two Conjunctive Normal Form

2016 ◽  
Vol 328 ◽  
pp. 31-45 ◽  
Author(s):  
Guillermo De Ita Luna ◽  
J. Raymundo Marcial-Romero ◽  
José A. Hernández
Keyword(s):  
Normal Form ◽  
Conjunctive Normal Form ◽  
Satisfiability Problem
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