DOCSLIB.ORG

Attack on a Scheme for Obfuscating and Outsourcing SAT Computations to the Cloud

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Attack on a Scheme for Obfuscating and Outsourcing SAT Computations to the Cloud Attack on a Scheme for Obfuscating and Outsourcing SAT Computations to the Cloud Khazam Alhamdan, Tassos Dimitriou and Imtiaz Ahmad Department of Computer Engineering, Kuwait University, Kuwait Keywords: SAT, Outsourcing Computations, Obfuscation, Data Privacy, Attack, Cloud Computing. Abstract: The emergence of cloud computing gave users the capability to offload computations that cannot be executed locally to cloud servers with large computational power. One such computationally demanding problem is solving large satisfiability (SAT) instances. Although many problems from AI, circuit verification, etc. can be converted to SAT, outsourcing SAT instances may leak considerable information that can put a user’s security at risk. Hence the privacy of outsourcing computations to the cloud is a major issue. In this work we look at the techniques of Qin et al. (Qin and Jia., 2014; Qin and Du., 2018) which have been used to obfuscate SAT formulas before they are released to the cloud. We came up with a realistic attack against their technique that demonstrates how a malicious cloud provider can obtain significant information about the underlying SAT instance. Our work shows that ad hoc schemes cannot offer the required security guarantees for outsourcing SAT computations, hence more formal frameworks should be used instead. 1 INTRODUCTION and Chen., 2018), graph theoretic problems (Blan- ton et al., 2013), rule-based machine learning (Wong Cloud computing is a new paradigm that enables ser- et al., 2007), and so on. For a recent survey on secu- vice providers to share resources (storage, computa- rity issues in computation outsourcing, please refer to tion, bandwidth, etc.) with users. Cloud computing (Shan et al., 2018). comes with mainly three different flavors: SaaS (Soft- Problems such as AI planning, deduction, and ware as a service), PaaS (Platform as a service), and software checking are also known to be hard espe- IaaS (Infrastructure as a service) (Mell and Grance, cially when the inputs are really large. Researchers 2011). While each model has its own usage, outsourc- use different algorithmic techniques to solve such ing computations mainly falls under the SaaS cate- problems, one of which it to reduce the problem from gory in which the provider offers the applications that its original form into a form (eg. propositional logic) can be run on the cloud, and the clients access these which can be tested for satisfiablity (SAT), i.e. find applications through an appropriate interface without an assignment to the variables that makes the formula having to worry about maintaining the actual hard- true (Hung and Gao., 2014). Once the problem is con- ware system. However, despite the increased conve- verted to a SAT instance, various optimized and well nience of cloud services, users may be reluctant to studied SAT solvers can be used to obtain the desired offload critical tasks to the cloud as this may leak pri- solution (Rintanen, 2011; Hung and Gao., 2014). vate information to the cloud provider. It is neces- Despite the advantage of reducing a difficult prob- sary therefore to protect user’s data and tasks against lem to such a well studied problem as SAT, still find- a malicious or untrusted provider (Zissis and Lekkas., ing a solution that satisfies the propositional logic 2012). problem is not easy. This problem is also known as There are already many problems that benefit she satisfiability problem (SAT). Knowing that SAT from outsourcing various computational tasks to the is hard means it typically requires a large amount of cloud such as those involving matrix multiplication computational power, which can be easily provided (Atallah and Frikken, 2010) and Linear Programming through the use of cloud services. Although outsourc- (C. Wang and Wang, 2011). Other known compu- ing computations to the cloud solves the problem of tationally demanding problems are those related to clients with limited computational resources to some modular exponentiation (Ding and Choo., 2017; Zhu extend, security issues arise since the input-output 356 Alhamdan, K., Dimitriou, T. and Ahmad, I. Attack on a Scheme for Obfuscating and Outsourcing SAT Computations to the Cloud. DOI: 10.5220/0007829503560362 In Proceedings of the 16th International Joint Conference on e-Business and Telecommunications (ICETE 2019), pages 356-362 ISBN: 978-989-758-378-0 Copyright c 2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved Attack on a Scheme for Obfuscating and Outsourcing SAT Computations to the Cloud relationship of SAT instances may reveal consider- ditional countermeasure that can be used to prevent able information about the user’s activities as cap- simple reverse engineering using a working chip. tured by the SAT formula. For example, SAT is of- Logic locking is a technique attempting to lock ten used as a tool to accomplish other goals; Wakrime the logical functionality of the circuit unless a certain (Wakrime, 2017) developed a system that considers key input is provided along with the input parameters sharing data in a privacy preserving manner using (Chakraborty and Bhunia., 2009) of the working pro- SAT. Brun et al. (Brun and Medvidovic., 2012) used totype. Roshanisefat et al. (Roshanisefat and Sasan., SAT as an abstract view of how computation privacy 2018) further introduced SRCLock (SAT-Resistant can be achieved on the cloud. Cyclic logic Locking) to overcome some weaknesses Our scope here is the privacy of the problem’s in the original practice of logic locking. However data, in particular of SAT formulas. One of the many Chen et al. (Chen, 2018) countered SRCLock by en- approaches to provide such service is by encrypt- hancing prior attacks against it. Yet, Xie et al. (Xie ing/disguising the original problem through a pro- and Srivastava., 2018) introduced a more complex cedure called obfuscation. However, a study per- way for circuit locking called Anti-SAT, which how- formed in (Hosseinzadeh and Leppanen.,¨ 2018) states ever has also been countered by the Bit-flipping attack that obfuscation increases the difficulty of reverse- in (Shen and Zhou., 2018). engineering the problem but it does not provide any The previous attacks demonstrate that is not easy guarantees for security. Here, we will exploit such po- to hide the functionality of a circuit. However, the tential weaknesses in the SAT obfuscation approach focus of this paper is to handle the computational pri- used in (Qin and Jia., 2014) and (Qin and Du., 2018). vacy aspect of the SAT problem which is about hid- More precisely, we developed an attack against ing the original SAT formula structure from the cloud the Qin et al. SAT obfuscation schemes and found solver. that a malicious provider may learn considerable in- Brun et al. (Brun and Medvidovic., 2012) pro- formation about the underlying SAT formula even if posed to distribute the computation of a SAT formula this is presented in an obfuscated form. The lesson on multiple machines such that every machine is as- to be learned is that if an obfuscation scheme is not signed to evaluate a different part of the formula. The designed carefully then solutions obtained might re- sub-evaluation is then passed to the neighbouring ma- veal enough information which can be used to de- chines. Although this method might work in theory, obfuscate and nullify the scheme. nothing prevents the servers from colluding in order The remaining of the paper is organized as fol- to recover the hidden formula. Hence this method as- lows. In Section 2, related work about privacy of SAT sumes a trustworthy cloud provider. instances is presented. In Section 3, the (Qin and Jia., Qin et al. in (Qin and Jia., 2014) and subsequently 2014) approach is described and our methodology to in (Qin and Du., 2018) proposed two similar meth- attack the scheme is discussed. In Section 4, we vali- ods that attempt to obfuscate a SAT formula by em- date our findings with further experimental evidence. bedding a secret key in them. In the next section we Finally, Section 5 concludes this work. describe their scheme as well as our attack against it. 2 RELATED WORK 3 ATTACKING THE QIN ET AL. SCHEMES There are two aspects of the SAT privacy problem, one focusing on hiding the circuit structure of a hard- We start with a brief discussion about the underlying ware design and the other focusing on the privacy of threat model and some background information on the solving computationally hard SAT instances. SAT problem. Then we describe how the target ob- Keshavarz et al. (Keshavarz and Holcomb., 2018) fuscation scheme works (Qin and Jia., 2014; Qin and surveyed the major techniques used to achieve intel- Du., 2018), and how our attack takes advantage of lectual property (IP) protection at the hardware level flaws in the scheme’s design. as well as their potential weaknesses. These include reverse engineering a circuit through imaging, using 3.1 Preliminaries a working chip, or analyzing the circuit at the logical level. A clever way of preventing the imaging attack Threat Model: There are two main participants in the is by disguising the gates in a way that they all look model of outsourcing computations to the cloud, the the same under imaging (Rajendran and Karri., 2013). cloud service provider and the user who wants to out- Adding more circuitry to the desired design is an ad- source his/her SAT instance to the cloud. The goal of 357 SECRYPT 2019 - 16th International Conference on Security and Cryptography any SAT obfuscation algorithm should be to prevent the variables of husk into clauses of the original for- the cloud solver from getting any information about mula in order to mix the two instances together and the original instance from the obfuscated one. As the wipe out any signature of the variables in the origi- cloud solver is assumed to have the computational ca- nal clauses.
Load more

Recommended publications
  • Chapter 2 Introduction to Classical Propositional
    CHAPTER 2 INTRODUCTION TO CLASSICAL PROPOSITIONAL LOGIC 1 Motivation and History The origins of the classical propositional logic, classical propositional calculus, as it was, and still often is called, go back to antiquity and are due to Stoic school of philosophy (3rd century B.C.), whose most eminent representative was Chryssipus. But the real development of this calculus began only in the mid-19th century and was initiated by the research done by the English math- ematician G. Boole, who is sometimes regarded as the founder of mathematical logic. The classical propositional calculus was ¯rst formulated as a formal ax- iomatic system by the eminent German logician G. Frege in 1879. The assumption underlying the formalization of classical propositional calculus are the following. Logical sentences We deal only with sentences that can always be evaluated as true or false. Such sentences are called logical sentences or proposi- tions. Hence the name propositional logic. A statement: 2 + 2 = 4 is a proposition as we assume that it is a well known and agreed upon truth. A statement: 2 + 2 = 5 is also a proposition (false. A statement:] I am pretty is modeled, if needed as a logical sentence (proposi- tion). We assume that it is false, or true. A statement: 2 + n = 5 is not a proposition; it might be true for some n, for example n=3, false for other n, for example n= 2, and moreover, we don't know what n is. Sentences of this kind are called propositional functions. We model propositional functions within propositional logic by treating propositional functions as propositions.
    [Show full text]
  • 12 Propositional Logic
    CHAPTER 12 ✦ ✦ ✦ ✦ Propositional Logic In this chapter, we introduce propositional logic, an algebra whose original purpose, dating back to Aristotle, was to model reasoning. In more recent times, this algebra, like many algebras, has proved useful as a design tool. For example, Chapter 13 shows how propositional logic can be used in computer circuit design. A third use of logic is as a data model for programming languages and systems, such as the language Prolog. Many systems for reasoning by computer, including theorem provers, program verifiers, and applications in the field of artificial intelligence, have been implemented in logic-based programming languages. These languages generally use “predicate logic,” a more powerful form of logic that extends the capabilities of propositional logic. We shall meet predicate logic in Chapter 14. ✦ ✦ ✦ ✦ 12.1 What This Chapter Is About Section 12.2 gives an intuitive explanation of what propositional logic is, and why it is useful. The next section, 12,3, introduces an algebra for logical expressions with Boolean-valued operands and with logical operators such as AND, OR, and NOT that Boolean algebra operate on Boolean (true/false) values. This algebra is often called Boolean algebra after George Boole, the logician who first framed logic as an algebra. We then learn the following ideas. ✦ Truth tables are a useful way to represent the meaning of an expression in logic (Section 12.4). ✦ We can convert a truth table to a logical expression for the same logical function (Section 12.5). ✦ The Karnaugh map is a useful tabular technique for simplifying logical expres- sions (Section 12.6).
    [Show full text]
  • Propositional Calculus
    CSC 438F/2404F Notes Winter, 2014 S. Cook REFERENCES The first two references have especially influenced these notes and are cited from time to time: [Buss] Samuel Buss: Chapter I: An introduction to proof theory, in Handbook of Proof Theory, Samuel Buss Ed., Elsevier, 1998, pp1-78. [B&M] John Bell and Moshe Machover: A Course in Mathematical Logic. North- Holland, 1977. Other logic texts: The first is more elementary and readable. [Enderton] Herbert Enderton: A Mathematical Introduction to Logic. Academic Press, 1972. [Mendelson] E. Mendelson: Introduction to Mathematical Logic. Wadsworth & Brooks/Cole, 1987. Computability text: [Sipser] Michael Sipser: Introduction to the Theory of Computation. PWS, 1997. [DSW] M. Davis, R. Sigal, and E. Weyuker: Computability, Complexity and Lan- guages: Fundamentals of Theoretical Computer Science. Academic Press, 1994. Propositional Calculus Throughout our treatment of formal logic it is important to distinguish between syntax and semantics. Syntax is concerned with the structure of strings of symbols (e.g. formulas and formal proofs), and rules for manipulating them, without regard to their meaning. Semantics is concerned with their meaning. 1 Syntax Formulas are certain strings of symbols as specified below. In this chapter we use formula to mean propositional formula. Later the meaning of formula will be extended to first-order formula. (Propositional) formulas are built from atoms P1;P2;P3;:::, the unary connective :, the binary connectives ^; _; and parentheses (,). (The symbols :; ^ and _ are read \not", \and" and \or", respectively.) We use P; Q; R; ::: to stand for atoms. Formulas are defined recursively as follows: Definition of Propositional Formula 1) Any atom P is a formula.
    [Show full text]
  • Why Would You Trust B? Eric Jaeger, Catherine Dubois
    Why Would You Trust B? Eric Jaeger, Catherine Dubois To cite this version: Eric Jaeger, Catherine Dubois. Why Would You Trust B?. Logic for Programming, Artificial In- telligence, and Reasoning, Nov 2007, Yerevan, Armenia. pp.288-302, 10.1007/978-3-540-75560-9. hal-00363345 HAL Id: hal-00363345 https://hal.archives-ouvertes.fr/hal-00363345 Submitted on 23 Feb 2009 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Why Would You Trust B? Eric´ Jaeger12 and Catherine Dubois3 1 LIP6, Universit´eParis 6, 4 place Jussieu, 75252 Paris Cedex 05, France 2 LTI, Direction centrale de la s´ecurit´edes syst`emes d’information, 51 boulevard de La Tour-Maubourg, 75700 Paris 07 SP, France 3 CEDRIC, Ecole´ nationale sup´erieure d’informatique pour l’industrie et l’entreprise, 18 all´ee Jean Rostand, 91025 Evry Cedex, France Abstract. The use of formal methods provides confidence in the cor- rectness of developments. Yet one may argue about the actual level of confidence obtained when the method itself – or its implementation – is not formally checked. We address this question for the B, a widely used formal method that allows for the derivation of correct programs from specifications.
    [Show full text]
  • An Introduction to Formal Methods for Philosophy Students
    An Introduction to Formal Methods for Philosophy Students Thomas Forster February 20, 2021 2 Contents 1 Introduction 13 1.1 What is Logic? . 13 1.1.1 Exercises for the first week: “Sheet 0” . 13 2 Introduction to Logic 17 2.1 Statements, Commands, Questions, Performatives . 18 2.1.1 Truth-functional connectives . 20 2.1.2 Truth Tables . 21 2.2 The Language of Propositional Logic . 23 2.2.1 Truth-tables for compound expressions . 24 2.2.2 Logical equivalence . 26 2.2.3 Non truth functional connectives . 27 2.3 Intension and Extension . 28 2.3.1 If–then . 31 2.3.2 Logical Form and Valid Argument . 33 2.3.3 The Type-Token Distinction . 33 2.3.4 Copies . 35 2.4 Tautology and Validity . 36 2.4.1 Valid Argument . 36 2.4.2 V and W versus ^ and _ .................... 40 2.4.3 Conjunctive and Disjunctive Normal Form . 41 2.5 Further Useful Logical Gadgetry . 46 2.5.1 The Analytic-Synthetic Distinction . 46 2.5.2 Necessary and Sufficient Conditions . 47 2.5.3 The Use-Mention Distinction . 48 2.5.4 Language-metalanguage distinction . 51 2.5.5 Semantic Optimisation and the Principle of Charity . 52 2.5.6 Inferring A-or-B from A . 54 2.5.7 Fault-tolerant pattern-matching . 54 2.5.8 Overinterpretation . 54 2.5.9 Affirming the consequent . 55 3 4 CONTENTS 3 Proof Systems for Propositional Logic 57 3.1 Arguments by LEGO . 57 3.2 The Rules of Natural Deduction . 57 3.2.1 Worries about reductio and hypothetical reasoning .
    [Show full text]
  • Vagueness at Every Order
    Vagueness at every order Andrew Bacon* May 4, 2020 Abstract There are some properties, like being bald, for which it is vague where the boundary between the things that have it, and the things that do not, lies. A number of argument threaten to show that such properties can still be associated with determinate and knowable boundaries: not between the things that have it and those that don't, but between the things such that it is borderline at some order whether they have it, and the things for which it is not. I argue that these arguments, if successful, turn on a contentious prin- ciple in the logic of determinacy: Brouwer's Principle, that every truth is determinately not determinately false. Other paradoxes which do not appear to turn on this principle often tacitly make assumptions about assertion, knowledge and higher order vagueness. In this paper I'll show how one can avoid sharp higher-order boundaries by rejecting these as- sumptions. I used to be a child, but now I am not. It follows, given classical logic, that I stopped being a child at some point. Indeed, there was a first nanosecond at which I stopped: a nanosecond before which I was a child (or unborn) but at which I was not a child. Although such a nanosecond exists, it is a vague matter when it occurred: it happened during a period when it was borderline whether I was a child. Different theories provide different accounts of what borderlineness consists in | perhaps it's ignorance, or semantic indecision, or something else.
    [Show full text]
  • Categorical Proof Theory of Classical Propositional Calculus
    Categorical Proof Theory of Classical Propositional Calculus Gianluigi Bellin Martin Hyland Edmund Robinson Christian Urban Queen Mary, University of London, UK University of Cambridge, UK Technical University of Munich (TUM), D Abstract We investigate semantics for classical proof based on the sequent calculus. We show that the propositional connectives are not quite well-behaved from a traditional categorical per- spective, and give a more refined, but necessarily complex, analysis of how connectives may be characterised abstractly. Finally we explain the consequences of insisting on more familiar categorical behaviour. Key words: classical logic, proof theory, category theory 1 Introduction In this paper we describe the shape of a semantics for classical proof in accord with Gentzen’s sequent calculus. For constructive proof we have the familiar correspondence between deductions in minimal logic and terms of a typed lambda calculus. Deductions in minimal logic (as in most constructive systems) reduce to a unique normal form, and around 1970 Per Martin-L¨of (see [18]) suggested using equality of normal forms as the identity criterion for proof objects in his constructive Type Theories: normal forms serve as the semantics of proof. But ¬ -normal forms for typed lambda calculus give maps in a free cartesian closed category; so we get a whole range of categorical models of constructive proof. This is the circle of connections surrounding the Curry-Howard isomorphism. We seek analogues of these ideas for classical proof. There are a number of immediate problems. The established term languages for classical proofs are either incompatible with the symmetries apparent in the sequent calculus (Parigot [16]) or in reconciling themselves to that symmetry at least make evaluation deterministic (cf Danos et al [5,21]).
    [Show full text]
  • Logical Derivability of the Concept of Meaning, Formulation I
    IOSR Journal of Humanities and Social Science (IOSRJHSS) ISSN: 2279-0845 Volume 1, Issue 5 (Sep-Oct 2012), PP 01-04 www.iosrjournals.org Logical Derivability of the Concept of Meaning, Formulation I Jonathan Chimakonam Okeke, Department of Philosophy,University of Calabar, Calabar, P. M. B 1115, Cross River State Nigeria ABSTRACT: Expressions, words and symbols without reference to something else which could be called their meanings are semantically helpless. But not all expressions and words refer; some even come with ambiguities and equivocations like Golden Mountain, Chimera etc., however, any symbol which does not refer could not properly be called a symbol. So because every symbol necessarily refers to something definite, it is not the case that ambiguities and equivocations would sneak into symbolic expressions. Hence, logic becomes that science which prefers symbolic or artificial or formal language to natural language. Therefore, since “meaning” or semantics is a central focus of logic together with syntax, we attempted in this work to obtain a logical derivation of it in the symbolic language of logic devoid of the ambiguities and equivocations of natural language. Keywords- language, logic, meaning, semantics, symbol, syntax. I. Introduction Meaning can be defined as having a fixed sense or conveying a fixed idea or a fixed thought. This means that having a transitory or tentative sense does not qualify as having meaning. In philosophy of language meaning is very crucial for our words and sentences will be useless if they contain no meaning. But meaning is not something peculiar to words or sentences alone, it can in similar way be extended to symbols or whatever stands as symbol.
    [Show full text]
  • Section 6.2 Propositional Calculus Propositional Calculus Is the Language of Propositions (Statements That Are True Or False)
    Section 6.2 Propositional Calculus Propositional calculus is the language of propositions (statements that are true or false). We represent propositions by formulas called well-formed formulas (wffs) that are constructed from an alphabet consisting of Truth symbols: T (or True) and F (or False) Propositional variables: uppercase letters. Connectives (operators): ¬ (not, negation) ∧ (and, conjunction) ∨ (or, disjunction) → (conditional, implication) Parentheses symbols: ( and ). A wff is either a truth symbol, a propositional variable, or if V and W are wffs, then so are ¬ V, V ∧ W, V ∨ W, V → W, and (W). Example. The expression A ¬ B is not a wff. But each of the following three expressions is a wff: A ∧ B → C, (A ∧ B) → C, and A ∧ (B → C). Truth Tables. The connectives are defined by the following truth tables. P Q ¬P P "Q P #Q P $ Q T T F T T T T F F F T F F T T F T T F F T F F T 1 ! Semantics The meaning of T (or True) is true and the meaning of F (or False) is false. The meaning of any other wff is its truth table, where in the absence of parentheses, we define the hierarchy of evaluation to be ¬, ∧, ∨, →, and we assume ∧, ∨, → are left associative. Examples. ¬ A ∧ B means (¬ A) ∧ B A ∨ B ∧ C means A ∨ (B ∧ C) A ∧ B → C means (A ∧ B) → C A → B → C means (A → B) → C. Three Classes A Tautology is a wff for which all truth table values are T. A Contradiction is a wff for which all truth table values are F.
    [Show full text]
  • Security Assessment of Dynamically Obfuscated Scan Chain Against Oracle-Guided Attacks
    Security Assessment of Dynamically Obfuscated Scan Chain Against Oracle-guided Attacks M SAZADUR RAHMAN, ADIB NAHIYAN, and FAHIM RAHMAN, University of Florida, USA SAVERIO FAZZARI, Booz Allen Hamilton, USA KENNETH PLAKS, Defense Advanced Research Projects Agency, USA FARIMAH FARAHMANDI, DOMENIC FORTE, and MARK TEHRANIPOOR, University of Florida, USA Logic locking has emerged as a promising solution to protect integrated circuits against piracy and tampering. However, the security provided by existing logic locking techniques is often thwarted by Boolean satisfiabil- ity (SAT)-based oracle-guided attacks. Criteria for successful SAT attacks on locked circuits include: (i) the circuit under attack is fully combinational, or (ii) the attacker has scan chain access. To address the threat posed by SAT-based attacks, we adopt the dynamically obfuscated scan chain (DOSC) architecture and il- lustrate its resiliency against the SAT attacks when inserted into the scan chain of an obfuscated design. We demonstrate, both mathematically and experimentally, that DOSC exponentially increases the resiliency against key extraction by SAT attack and its variants. Our results show that the mathematical estimation of attack complexity correlates to the experimental results with an accuracy of 95% or better. Along with the formal proof, we model DOSC architecture to its equivalent combinational circuit and perform SAT attack to evaluate its resiliency empirically. Our experiments demonstrate that SAT attack on DOSC-inserted bench- mark circuits timeout at minimal test time overhead, and while DOSC requires less than 1% area and power overhead. CCS Concepts: • Security and privacy → Security in hardware; Hardware security implementation; Hardware-based security protocols; Additional Key Words and Phrases: SAT attack, logic locking, scan obfuscation, mathematical model for sat- isfiability, hardware obfuscation 29 ACM Reference format: M Sazadur Rahman, Adib Nahiyan, Fahim Rahman, Saverio Fazzari, Kenneth Plaks, Farimah Farahmandi, Domenic Forte, and Mark Tehranipoor.
    [Show full text]
  • Predicate Calculus
    Predicate Calculus (Alternative names: predicate logic, first order logic, elementary logic, restricted predicate calculus, restricted functional calculus, relational calculus, theory of quantification, theory of quantification with equality, etc.) In propositional logic only the logical forms of compound propositions are analyzed. A simple proposition is an unanalyzed whole which is either true or false. There are certain arguments that seem to be perfectly logical, yet they cannot be expressed by using propositional calculus. 1 Example 1. All cats have tails. 2. Tom is a cat. From these two sentences, one should be able to conclude that 3. Tom has a tail. To show that this argument is sound, we must be able to identify individuals, such as Tom, together with their properties and predicates. This is the objective of predicate calculus. 2 • Generally, predicates are used to describe certain properties or relationships between individuals or objects. Example: In \Mary and Jane are sisters", the phrase \are sisters" is a predicate. The entities connected this way, Mary and Jane, are called terms. • Terms play a similar role in predicate calculus as nouns and pronouns do in the English language. • In addition to terms and predicates, one uses quantifiers. Quantifiers indicate how frequently a certain statement is true. Specifically, the universal quantifier is used to indicate that a statement is always true, whereas the existential quantifier indicates that a statement is sometimes true. Example: In \All cats have tails", the word \all" indicates that the statement \cats have tails" is universally true. • Predicate calculus is a generalization of propositional calculus. Hence, besides terms, predicates, and quantifiers, predicate calculus contains propositional variables, constants and connectives as part of the language.
    [Show full text]
  • Identification of Formal Fallacies in a Natural Dialogue
    Identification of Formal Fallacies in a Natural Dialogue Magdalena Kacprzak1 and Anna Sawicka2 1 Faculty of Computer Science, BialystokUniversity of Technology, Poland 2 Faculty of Computer Science, Polish-Japanese Institute of Information Technology, Warsaw, Poland Abstract. This paper is a continuation of the work presented at CS&P 2012 where the LND dialogue system was proposed. It brings together and unifies two traditions in studying dialogue as a game: the dialogical logic introduced by Lorenzen and persuasion dialogue games as specified by Prakken. The aim of the system LND is to recognize and verify formal fallacies in dialogues. Now we extend this system with a new protocol which allows for reconstruction of natural dialogues in which parties can be committed to formal fallacies. Finally, we show the implementation of the applied protocols. Keywords: protocol for dialogue games, natural dialogue, formal fal- lacy, Lorenzen Natural Dialogue 1 Introduction In [19], Yaskorska, Budzynska and Kacprzak proposed a protocol, called LND, for verifying during a dialogue whether a propositional formula is a tautology. This protocol is based on Lorenzen's dialogical logic [7, 8, 15]. The aim of this protocol is to use it in a game simulating natural dialogue as an inference scheme valida- tor. Participants of dialogues perform a variety of actions. Some of them can be recognized as justification of player's standpoint. Such an argumentation may refer to argumentation schemes based on propositional tautologies. The LND game tests propositional formulas and thereby decides whether a corresponding inference is correct. The contribution of the present work is to introduce a dia- logue system, called PND, in which players are allowed to make formal fallacies, that is, those that use schemes which are not equivalent to a valid formulas of the underlying logic.
    [Show full text]